fof(t51_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v10_incproj(k13_afproj(A)) => v4_aff_2(A) ) ) ), inference(mizar_proof,[status(thm)],[t8_aff_4,t9_aff_4,t30_aff_1,d3_aff_1,t26_aff_1,t51_aff_1,t40_aff_4,t20_afproj,t23_afproj,t23_afproj,t20_afproj,t26_afproj,t26_afproj,t7_mcart_1,t7_mcart_1,d9_incproj,d9_incproj,d13_incproj,t26_afproj,d8_incproj,t26_afproj,t30_afproj,t26_afproj,t28_afproj,d8_incproj,t7_mcart_1,t7_mcart_1,t7_mcart_1,t7_mcart_1,d5_incproj,d19_incproj,d8_incproj,t11_afproj,t58_aff_1,t58_aff_1,t59_aff_1,t53_aff_1,t21_afproj,d1_incsp_1,t41_afproj,t24_afproj,t27_afproj,t20_afproj,t28_afproj,t40_aff_4,t58_aff_1,t53_aff_1,t50_afproj,t65_aff_1,d4_aff_2]), [file(afproj,t51_afproj),interesting(1.00)]). fof(t49_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v11_incproj(k13_afproj(A)) => v2_aff_2(A) ) ) ), inference(mizar_proof,[status(thm)],[t38_aff_4,t20_afproj,t23_afproj,t23_afproj,t26_aff_1,t30_aff_1,d3_aff_1,t51_aff_1,t40_aff_4,t23_afproj,t20_afproj,t26_afproj,t26_afproj,t28_afproj,t30_afproj,t26_afproj,t19_aff_4,t31_afproj,t14_aff_1,t9_aff_4,t9_aff_4,d6_incproj,d6_incproj,t7_mcart_1,t7_mcart_1,t26_afproj,l56_afproj,d9_incproj,d13_incproj,d8_incproj,d7_incproj,d20_incproj,t27_afproj,t20_afproj,t28_afproj,t40_aff_4,t58_aff_1,t53_aff_1,t48_afproj,d2_aff_2]), [file(afproj,t49_afproj),interesting(0.98)]). fof(t52_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v9_incproj(k13_afproj(A)) => v1_translac(A) ) ) ), inference(mizar_proof,[status(thm)],[t20_afproj,t11_aff_1,t12_aff_1,t26_aff_1,d2_aff_1,d1_aff_1,d2_aff_1,t15_aff_1,d1_aff_1,t13_aff_1,d1_aff_1,t15_aff_1,d1_aff_1,t13_aff_1,d1_aff_1,t15_aff_1,d1_aff_1,t13_aff_1,d3_aff_1,t51_aff_1,t40_aff_4,t23_afproj,t20_afproj,t38_aff_4,t23_afproj,d3_aff_4,t28_aff_4,t19_aff_4,t26_afproj,t28_afproj,t30_afproj,t26_afproj,t28_afproj,t30_afproj,t31_afproj,t26_afproj,t59_aff_1,t26_afproj,t59_aff_1,t26_afproj,t59_aff_1,t26_afproj,t59_aff_1,d8_incproj,d7_incproj,d18_incproj,d5_papdesaf]), [file(afproj,t52_afproj),interesting(0.89)]). fof(t46_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( ~ ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_incproj(k14_afproj(A)) & v2_incproj(k14_afproj(A)) & v3_incproj(k14_afproj(A)) & v4_incproj(k14_afproj(A)) & v5_incproj(k14_afproj(A)) & l1_incsp_1(k14_afproj(A)) ) ) ) ), inference(mizar_proof,[status(thm)],[t38_afproj,t40_afproj,l55_afproj,t39_afproj,t44_afproj,d9_incproj,d10_incproj,d11_incproj,d12_incproj,d13_incproj]), [file(afproj,t46_afproj),interesting(0.88)]). fof(t16_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => r1_subset_1(u1_struct_0(A),k7_afproj(A)) ) ), inference(mizar_proof,[status(thm)],[t3_xboole_0,t14_afproj,t27_aff_4,d3_aff_4,t40_aff_4,t9_afproj,d3_aff_4]), [file(afproj,t16_afproj),interesting(0.81)]). fof(t2_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) & v1_aff_4(B,A) ) => B = u1_struct_0(A) ) ) ) ), inference(mizar_proof,[status(thm)],[t1_afproj,t33_aff_4]), [file(afproj,t2_afproj),interesting(0.80)]). fof(t1_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) & B = u1_struct_0(A) ) => v1_aff_4(B,A) ) ) ) ), inference(mizar_proof,[status(thm)],[t21_aff_1,t16_aff_1,t26_aff_1,d3_aff_1,t59_aff_1,t33_aff_1,d2_aff_4,t27_aff_4,d3_aff_4,t58_aff_1,t72_aff_1,t54_aff_1,d1_aff_4,d3_tarski,d10_xboole_0]), [file(afproj,t1_afproj),interesting(0.79)]). fof(t3_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) & v1_aff_4(B,A) & v1_aff_4(C,A) ) => B = C ) ) ) ) ), inference(mizar_proof,[status(thm)],[t2_afproj]), [file(afproj,t3_afproj),interesting(0.76)]). fof(t45_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v6_incproj(k13_afproj(A)) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) ) ) ), inference(mizar_proof,[status(thm)],[t37_aff_4,t48_aff_4,t26_aff_1,d3_aff_1,t23_afproj,d14_incproj,t27_afproj,t20_afproj,t28_afproj,t29_afproj,t40_aff_4,t56_aff_4,t43_aff_4]), [file(afproj,t45_afproj),interesting(0.74)]). fof(t17_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => r1_xboole_0(k1_afproj(A),k8_afproj(A)) ) ) ), inference(mizar_proof,[status(thm)],[t3_xboole_0,t1_afproj,t15_afproj,t31_aff_1,t10_afproj,t33_aff_4]), [file(afproj,t17_afproj),interesting(0.73)]). fof(t22_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => m1_subset_1(B,u1_incsp_1(k13_afproj(A))) ) ) ), inference(mizar_proof,[status(thm)],[t21_afproj,t20_afproj]), [file(afproj,t22_afproj),interesting(0.70)]). fof(l60_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k13_afproj(A))) => r1_incsp_1(k13_afproj(A),B,C) ) ) ) ), inference(mizar_proof,[status(thm)],[t21_aff_1,t16_aff_1,d3_aff_1,t20_afproj,t23_afproj,t26_afproj,t26_aff_1,t33_aff_1]), [file(afproj,l60_afproj),interesting(0.67)]). fof(l58_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ? [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) & r1_incsp_1(k13_afproj(A),B,D) & r1_incsp_1(k13_afproj(A),C,D) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t11_aff_4,t23_afproj,t26_afproj,t27_aff_4,d3_aff_4,t23_afproj,t26_afproj,d3_aff_4,t40_aff_4,t28_afproj,t20_afproj,t27_aff_4,d3_aff_4,t23_afproj,d3_aff_4,t40_aff_4,t28_afproj,t26_afproj,t31_aff_1,t27_aff_4,d3_aff_4,t38_aff_4,t23_afproj,t41_aff_4,t42_aff_4,t29_afproj,t20_afproj,t20_afproj]), [file(afproj,l58_afproj),interesting(0.65)]). fof(t15_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k8_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k6_afproj(A,C) & v1_aff_4(C,A) ) ) ) ), inference(mizar_proof,[status(thm)],[d5_eqrel_1,d6_afproj,d6_afproj,d5_eqrel_1]), [file(afproj,t15_afproj),interesting(0.64)]). fof(t25_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k14_afproj(A))) => m1_subset_1(k4_tarski(B,2),u2_incsp_1(k13_afproj(A))) ) ) ), inference(mizar_proof,[status(thm)],[t24_afproj,t23_afproj]), [file(afproj,t25_afproj),interesting(0.62)]). fof(t14_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k7_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k5_afproj(A,C) & v1_aff_1(C,A) ) ) ) ), inference(mizar_proof,[status(thm)],[d5_eqrel_1,d5_afproj,d5_afproj,d5_eqrel_1]), [file(afproj,t14_afproj),interesting(0.61)]). fof(l59_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k13_afproj(A))) => ~ ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) & ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),D,B) & r1_incsp_1(k13_afproj(A),D,C) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t23_afproj,t23_afproj,t2_afproj,l57_afproj,t3_afproj,t42_aff_4,t55_aff_1,t40_aff_4,t20_afproj,t28_afproj,t29_afproj,t2_afproj,t42_aff_4,t55_aff_1,t40_aff_4,t20_afproj,t28_afproj,t29_afproj,t20_afproj,t11_afproj,t55_aff_1,t40_aff_4,t28_afproj,t72_aff_1,t20_afproj,t26_afproj]), [file(afproj,l59_afproj),interesting(0.61)]). fof(t41_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) => ~ ( B != C & r2_hidden(k4_tarski(B,D),u3_incsp_1(k13_afproj(A))) & r2_hidden(k4_tarski(C,D),u3_incsp_1(k13_afproj(A))) & ! [E] : ( m1_subset_1(E,u2_incsp_1(k14_afproj(A))) => D != k4_tarski(E,2) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t22_afproj,d1_incsp_1,t21_afproj,t21_afproj,t40_afproj,t24_afproj,t25_afproj,t36_afproj,t29_afproj,l56_afproj]), [file(afproj,t41_afproj),interesting(0.57)]). fof(t21_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k5_afproj(A,C) & v1_aff_1(C,A) ) ) ) ), inference(mizar_proof,[status(thm)],[t14_afproj]), [file(afproj,t21_afproj),interesting(0.56)]). fof(t24_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k14_afproj(A))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k6_afproj(A,C) & v1_aff_4(C,A) ) ) ) ), inference(mizar_proof,[status(thm)],[t15_afproj]), [file(afproj,t24_afproj),interesting(0.56)]). fof(t18_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k2_zfmisc_1(k1_afproj(A),k1_tarski(1))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k4_tarski(C,1) & v1_aff_1(C,A) ) ) ) ), inference(mizar_proof,[status(thm)],[d2_zfmisc_1,d1_tarski,t129_zfmisc_1]), [file(afproj,t18_afproj),interesting(0.54)]). fof(t47_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ( v1_incproj(k14_afproj(A)) & v2_incproj(k14_afproj(A)) & v3_incproj(k14_afproj(A)) & v4_incproj(k14_afproj(A)) & v5_incproj(k14_afproj(A)) & l1_incsp_1(k14_afproj(A)) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) ) ), inference(mizar_proof,[status(thm)],[d11_incproj,t21_afproj,t24_afproj,t2_afproj,t42_aff_4,t36_afproj]), [file(afproj,t47_afproj),interesting(0.53)]). fof(t19_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k2_zfmisc_1(k8_afproj(A),k1_tarski(2))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k4_tarski(k6_afproj(A,C),2) & v1_aff_4(C,A) ) ) ) ), inference(mizar_proof,[status(thm)],[d2_zfmisc_1,t15_afproj,d1_tarski,t15_afproj,t129_zfmisc_1]), [file(afproj,t19_afproj),interesting(0.47)]). fof(t30_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_1(B,A) & C = k5_afproj(A,B) & D = k4_tarski(B,1) ) => r1_incsp_1(k13_afproj(A),C,D) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t55_aff_1,t40_aff_4,t28_afproj]), [file(afproj,t30_afproj),interesting(0.46)]). fof(t26_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( B = D & k4_tarski(C,1) = E ) => ( r1_incsp_1(k13_afproj(A),D,E) <=> ( v1_aff_1(C,A) & r2_hidden(B,C) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_incsp_1,t7_mcart_1,t7_mcart_1,t14_afproj,d3_xboole_0,d7_xboole_0,t16_afproj,t33_zfmisc_1,d11_afproj,d11_afproj,d1_incsp_1]), [file(afproj,t26_afproj),interesting(0.43)]). fof(t23_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k13_afproj(A))) <=> ~ ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ~ ( B = k4_tarski(C,1) & v1_aff_1(C,A) ) & ~ ( B = k4_tarski(k6_afproj(A,C),2) & v1_aff_4(C,A) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t18_afproj,t19_afproj,d2_xboole_0,t18_afproj,d2_xboole_0,t19_afproj,d2_xboole_0]), [file(afproj,t23_afproj),interesting(0.42)]). fof(t27_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ~ ( B = D & k4_tarski(k6_afproj(A,C),2) = E & v1_aff_4(C,A) & r1_incsp_1(k13_afproj(A),D,E) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_incsp_1,t7_mcart_1,t7_mcart_1,t14_afproj,d3_xboole_0,d7_xboole_0,t16_afproj,d11_afproj]), [file(afproj,t27_afproj),interesting(0.41)]). fof(t34_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) => ( ( D = k4_tarski(B,1) & v1_aff_1(B,A) & r1_incsp_1(k13_afproj(A),C,D) ) => ( m1_subset_1(C,u1_struct_0(A)) | C = k5_afproj(A,B) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t20_afproj,t28_afproj,t12_afproj]), [file(afproj,t34_afproj),interesting(0.41)]). fof(t28_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( D = k5_afproj(A,B) & k4_tarski(C,1) = E & v1_aff_1(B,A) & v1_aff_1(C,A) ) => ( r1_incsp_1(k13_afproj(A),D,E) <=> r1_aff_4(A,B,C) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_incsp_1,t33_zfmisc_1,t7_afproj,t14_afproj,d3_xboole_0,d7_xboole_0,t16_afproj,d5_afproj,t31_eqrel_1,t9_afproj,t40_aff_4,t40_aff_4,t33_zfmisc_1,d11_afproj,t9_afproj,d5_afproj,t7_afproj,t31_eqrel_1,d5_afproj,d11_afproj,d1_incsp_1]), [file(afproj,t28_afproj),interesting(0.39)]). fof(t35_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( E = k4_tarski(B,1) & v1_aff_1(B,A) & r1_incsp_1(k13_afproj(A),C,E) & r1_incsp_1(k13_afproj(A),D,E) ) => ( D = C | m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(D,u1_struct_0(A)) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t34_afproj]), [file(afproj,t35_afproj),interesting(0.36)]). fof(t36_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k14_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k14_afproj(A))) => ( ( D = k5_afproj(A,B) & E = k6_afproj(A,C) & v1_aff_1(B,A) & v1_aff_4(C,A) ) => ( r1_incsp_1(k14_afproj(A),D,E) <=> r1_aff_4(A,B,C) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d12_afproj,d1_incsp_1,d1_incsp_1,d12_afproj,t11_afproj,t13_afproj,t56_aff_4,t59_aff_4,t60_aff_4]), [file(afproj,t36_afproj),interesting(0.34)]). fof(t33_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) => ~ ( D = k4_tarski(k6_afproj(A,B),2) & v1_aff_4(B,A) & r1_incsp_1(k13_afproj(A),C,D) & m1_subset_1(C,u1_struct_0(A)) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t27_afproj]), [file(afproj,t33_afproj),interesting(0.31)]). fof(t31_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_1(B,A) & v1_aff_4(C,A) & r1_tarski(B,C) & D = k5_afproj(A,B) & E = k4_tarski(k6_afproj(A,C),2) ) => r1_incsp_1(k13_afproj(A),D,E) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t42_aff_4,t29_afproj]), [file(afproj,t31_afproj),interesting(0.30)]). fof(t29_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( D = k5_afproj(A,B) & E = k4_tarski(k6_afproj(A,C),2) & v1_aff_1(B,A) & v1_aff_4(C,A) ) => ( r1_incsp_1(k13_afproj(A),D,E) <=> r1_aff_4(A,B,C) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_incsp_1,t33_zfmisc_1,t33_zfmisc_1,t7_afproj,t8_afproj,d5_afproj,t31_eqrel_1,t9_afproj,d6_afproj,t31_eqrel_1,t10_afproj,t40_aff_4,t56_aff_4,t59_aff_4,t60_aff_4,d11_afproj,d11_afproj,d1_incsp_1]), [file(afproj,t29_afproj),interesting(0.28)]). fof(t43_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u2_incsp_1(k13_afproj(A))) => ~ ( v1_aff_4(B,A) & v1_aff_1(C,A) & v1_aff_1(D,A) & r1_tarski(C,B) & r1_tarski(D,B) & E = k4_tarski(C,1) & F = k4_tarski(D,1) & ! [G] : ( m1_subset_1(G,u1_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),G,E) & r1_incsp_1(k13_afproj(A),G,F) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t11_afproj,t20_afproj,t30_afproj,t20_afproj,t26_afproj,t22_aff_4]), [file(afproj,t43_afproj),interesting(0.24)]). fof(t32_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_4(B,A) & r1_tarski(C,B) & r4_aff_1(A,D,C) & E = k5_afproj(A,D) & F = k4_tarski(k6_afproj(A,B),2) ) => r1_incsp_1(k13_afproj(A),E,F) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t50_aff_1,t42_aff_4,t56_aff_4,t29_afproj]), [file(afproj,t32_afproj),interesting(0.20)]). fof(l63_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u1_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u1_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ! [K] : ( m1_subset_1(K,u2_incsp_1(k13_afproj(A))) => ! [L] : ( m1_subset_1(L,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_1(C,A) & v1_aff_1(D,A) & v1_aff_4(E,A) & r1_tarski(C,E) & r1_tarski(D,E) & B = G & J = k4_tarski(C,1) & K = k4_tarski(D,1) & r1_incsp_1(k13_afproj(A),H,J) & r1_incsp_1(k13_afproj(A),I,K) & r1_incsp_1(k13_afproj(A),H,L) & r1_incsp_1(k13_afproj(A),I,L) & L = k4_tarski(F,1) & v1_aff_1(F,A) ) => ( J = K | H = I | r1_tarski(F,E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t26_afproj,t26_afproj,t71_aff_1,t19_aff_4,t26_afproj,t28_afproj,t40_aff_4,t28_afproj,t40_aff_4,t58_aff_1,d3_aff_4,t28_aff_4,t20_afproj,t26_afproj,t28_afproj,t40_aff_4,t28_afproj,t40_aff_4,t58_aff_1,d3_aff_4,t28_aff_4,t28_afproj,t40_aff_4,t58_aff_1,t11_afproj,t20_afproj,t20_afproj]), [file(afproj,l63_afproj),interesting(0.13)]). fof(t11_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r2_hidden(C,D) & v1_aff_1(D,A) ) ) ) ) ), file(aff_4,t11_aff_4), [interesting(0.00)]). fof(d2_zfmisc_1,definition,( ! [A,B,C] : ( C = k2_zfmisc_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E,F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k4_tarski(E,F) ) ) ) ), file(zfmisc_1,d2_zfmisc_1), [interesting(0.00)]). fof(d1_tarski,definition,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), [interesting(0.00)]). fof(t129_zfmisc_1,theorem,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <=> ( r2_hidden(A,C) & B = D ) ) ), file(zfmisc_1,t129_zfmisc_1), [interesting(0.00)]). fof(d5_eqrel_1,definition,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k7_eqrel_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,A) & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ), file(eqrel_1,d5_eqrel_1), [interesting(0.00)]). fof(d6_afproj,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(B,A) => k6_afproj(A,B) = k6_eqrel_1(k2_afproj(A),k4_afproj(A),B) ) ) ) ), file(afproj,d6_afproj), [interesting(0.00)]). fof(d2_xboole_0,definition,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), [interesting(0.00)]). fof(d1_incsp_1,definition,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ( r1_incsp_1(A,B,C) <=> r2_hidden(k1_domain_1(u1_incsp_1(A),u2_incsp_1(A),B,C),u3_incsp_1(A)) ) ) ) ) ), file(incsp_1,d1_incsp_1), [interesting(0.00)]). fof(t7_mcart_1,theorem,( ! [A,B] : ( k1_mcart_1(k4_tarski(A,B)) = A & k2_mcart_1(k4_tarski(A,B)) = B ) ), file(mcart_1,t7_mcart_1), [interesting(0.00)]). fof(d5_afproj,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) => k5_afproj(A,B) = k6_eqrel_1(k1_afproj(A),k3_afproj(A),B) ) ) ) ), file(afproj,d5_afproj), [interesting(0.00)]). fof(d3_xboole_0,definition,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), [interesting(0.00)]). fof(d7_xboole_0,definition,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), [interesting(0.00)]). fof(t3_xboole_0,theorem,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), [interesting(0.00)]). fof(t27_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(C,A) => v1_aff_1(k2_aff_4(A,B,C),A) ) ) ) ) ), file(aff_4,t27_aff_4), [interesting(0.00)]). fof(d3_aff_4,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k2_aff_4(A,B,C) <=> ( r2_hidden(B,D) & r4_aff_1(A,C,D) ) ) ) ) ) ) ) ), file(aff_4,d3_aff_4), [interesting(0.00)]). fof(t40_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(B,A) & v1_aff_1(C,A) ) => ( r4_aff_1(A,B,C) <=> r1_aff_4(A,B,C) ) ) ) ) ) ), file(aff_4,t40_aff_4), [interesting(0.00)]). fof(t27_eqrel_1,theorem,( ! [A,B,C,D] : ( ( v1_relat_2(D) & v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) ) => ( r2_hidden(B,k6_eqrel_1(A,D,C)) <=> r2_hidden(k4_tarski(B,C),D) ) ) ), file(eqrel_1,t27_eqrel_1), [interesting(0.00)]). fof(t33_zfmisc_1,theorem,( ! [A,B,C,D] : ( k4_tarski(A,B) = k4_tarski(C,D) => ( A = C & B = D ) ) ), file(zfmisc_1,t33_zfmisc_1), [interesting(0.00)]). fof(t9_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) => ! [C] : ( r2_hidden(C,k5_afproj(A,B)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = D & v1_aff_1(D,A) & r1_aff_4(A,B,D) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d5_afproj,t27_eqrel_1,t33_zfmisc_1,t40_aff_4,t40_aff_4,t40_aff_4,t40_aff_4,t27_eqrel_1,d5_afproj]), [file(afproj,t9_afproj),interesting(0.00)]). fof(d11_afproj,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m2_relset_1(B,k9_afproj(A),k10_afproj(A)) => ( B = k11_afproj(A) <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),B) <=> ~ ( ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(E,A) & D = k4_tarski(E,1) & ( ( r2_hidden(C,u1_struct_0(A)) & r2_hidden(C,E) ) | C = k5_afproj(A,E) ) ) ) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(E,A) & v1_aff_4(F,A) & C = k5_afproj(A,E) & D = k4_tarski(k6_afproj(A,F),2) & r1_aff_4(A,E,F) ) ) ) ) ) ) ) ) ), file(afproj,d11_afproj), [interesting(0.00)]). fof(t7_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k1_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = C & v1_aff_1(C,A) ) ) ) ), file(afproj,t7_afproj), [interesting(0.00)]). fof(t31_eqrel_1,theorem,( ! [A,B,C] : ( ( v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) ) => ! [D] : ( r2_hidden(D,A) => ( r2_hidden(B,k6_eqrel_1(A,C,D)) <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ), file(eqrel_1,t31_eqrel_1), [interesting(0.00)]). fof(t20_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) <=> ~ ( ~ m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B = k5_afproj(A,C) & v1_aff_1(C,A) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t14_afproj,d2_xboole_0,d2_xboole_0,t14_afproj,d2_xboole_0]), [file(afproj,t20_afproj),interesting(0.00)]). fof(t31_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D ) ) ) ) ) ) ), file(aff_1,t31_aff_1), [interesting(0.00)]). fof(t38_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,C) & r2_hidden(B,D) & v1_aff_1(C,A) & v1_aff_1(D,A) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,E) & r1_tarski(D,E) & v1_aff_4(E,A) ) ) ) ) ) ) ) ), file(aff_4,t38_aff_4), [interesting(0.00)]). fof(t41_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(B,A) & v1_aff_4(C,A) ) => ( r1_aff_4(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(D,C) & ( r4_aff_1(A,B,D) | r4_aff_1(A,D,B) ) ) ) ) ) ) ) ), file(aff_4,t41_aff_4), [interesting(0.00)]). fof(t42_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(B,A) & v1_aff_4(C,A) & r1_tarski(B,C) ) => r1_aff_4(A,B,C) ) ) ) ) ), file(aff_4,t42_aff_4), [interesting(0.00)]). fof(t8_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k2_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = C & v1_aff_4(C,A) ) ) ) ), file(afproj,t8_afproj), [interesting(0.00)]). fof(t58_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(B,A) & v1_aff_4(C,A) & r1_aff_4(A,B,C) ) => r1_aff_4(A,C,B) ) ) ) ) ), file(aff_4,t58_aff_4), [interesting(0.00)]). fof(t10_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(B,A) => ! [C] : ( r2_hidden(C,k6_afproj(A,B)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = D & v1_aff_4(D,A) & r1_aff_4(A,B,D) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d6_afproj,t27_eqrel_1,t33_zfmisc_1,t58_aff_4,t58_aff_4,t27_eqrel_1,d6_afproj]), [file(afproj,t10_afproj),interesting(0.00)]). fof(t56_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r4_aff_1(A,B,C) & r1_aff_4(A,C,D) ) => r1_aff_4(A,B,D) ) ) ) ) ) ), file(aff_4,t56_aff_4), [interesting(0.00)]). fof(t59_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(B,A) & B = k1_xboole_0 ) ) ) ), file(aff_4,t59_aff_4), [interesting(0.00)]). fof(t60_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_aff_4(A,B,C) & r1_aff_4(A,C,D) ) => ( C = k1_xboole_0 | r1_aff_4(A,B,D) ) ) ) ) ) ) ), file(aff_4,t60_aff_4), [interesting(0.00)]). fof(t21_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_aff_1(A,B,C,D) ) ) ) ) ), file(aff_1,t21_aff_1), [interesting(0.00)]). fof(t16_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_aff_1(A,B,B,C) & r1_aff_1(A,B,C,C) & r1_aff_1(A,B,C,B) ) ) ) ) ), file(aff_1,t16_aff_1), [interesting(0.00)]). fof(t26_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k2_aff_1(A,B,C)) & r2_hidden(C,k2_aff_1(A,B,C)) ) ) ) ) ), file(aff_1,t26_aff_1), [interesting(0.00)]). fof(d3_aff_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C != D & B = k2_aff_1(A,C,D) ) ) ) ) ) ), file(aff_1,d3_aff_1), [interesting(0.00)]). fof(t59_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r4_aff_1(A,C,D) & r2_hidden(B,C) & r2_hidden(B,D) ) => C = D ) ) ) ) ) ), file(aff_1,t59_aff_1), [interesting(0.00)]). fof(t33_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & v1_aff_1(E,A) & r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) ) ) ) ) ) ) ), file(aff_1,t33_aff_1), [interesting(0.00)]). fof(d2_aff_4,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v1_aff_1(C,A) & v1_aff_1(D,A) & ~ r4_aff_1(A,C,D) & B = k1_aff_4(A,C,D) ) ) ) ) ) ), file(aff_4,d2_aff_4), [interesting(0.00)]). fof(t58_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ~ ( ~ ( r4_aff_1(A,B,C) & r4_aff_1(A,C,D) ) & ~ ( r4_aff_1(A,B,C) & r4_aff_1(A,D,C) ) & ~ ( r4_aff_1(A,C,B) & r4_aff_1(A,C,D) ) & ~ ( r4_aff_1(A,C,B) & r4_aff_1(A,D,C) ) ) => r4_aff_1(A,B,D) ) ) ) ) ) ), file(aff_1,t58_aff_1), [interesting(0.00)]). fof(t72_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(B,A) & v1_aff_1(C,A) & ~ r4_aff_1(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) ) ) ) ), file(aff_1,t72_aff_1), [interesting(0.00)]). fof(t54_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,D) & r2_hidden(C,D) & r3_aff_1(A,D,E) ) => r2_aff_1(A,B,C,E) ) ) ) ) ) ) ), file(aff_1,t54_aff_1), [interesting(0.00)]). fof(d1_aff_4,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k1_aff_4(A,B,C) = a_3_0_aff_4(A,B,C) ) ) ) ), file(aff_4,d1_aff_4), [interesting(0.00)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.00)]). fof(d10_xboole_0,definition,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), [interesting(0.00)]). fof(t33_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => ( ( ~ ( v1_aff_1(B,A) & v1_aff_1(C,A) ) & ~ ( v1_aff_4(B,A) & v1_aff_4(C,A) ) ) | B = C ) ) ) ) ) ), file(aff_4,t33_aff_4), [interesting(0.00)]). fof(t55_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) => r3_aff_1(A,B,B) ) ) ) ), file(aff_1,t55_aff_1), [interesting(0.00)]). fof(t34_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(E,B) & ~ r1_aff_1(A,C,D,E) ) ) ) ) ) ) ) ), file(aff_4,t34_aff_4), [interesting(0.00)]). fof(t19_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(D,A) & r2_hidden(B,D) & r2_hidden(C,D) ) => ( B = C | r1_tarski(k2_aff_1(A,B,C),D) ) ) ) ) ) ) ), file(aff_4,t19_aff_4), [interesting(0.00)]). fof(t11_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(B,A) & v1_aff_1(C,A) ) => ( k5_afproj(A,B) = k5_afproj(A,C) <=> r4_aff_1(A,B,C) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d5_afproj,t31_eqrel_1,t9_afproj,t40_aff_4,t40_aff_4,t9_afproj,t31_eqrel_1]), [file(afproj,t11_afproj),interesting(0.00)]). fof(l57_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k13_afproj(A))) => ? [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) & ? [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) & ? [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) & r1_incsp_1(k13_afproj(A),C,B) & r1_incsp_1(k13_afproj(A),D,B) & r1_incsp_1(k13_afproj(A),E,B) & C != D & D != E & E != C ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t23_afproj,t31_aff_1,t20_afproj,t20_afproj,t55_aff_1,t40_aff_4,t26_afproj,t28_afproj,t14_afproj,d3_xboole_0,d7_xboole_0,t16_afproj,t34_aff_4,t16_aff_1,d3_aff_1,t20_afproj,t19_aff_4,t42_aff_4,t29_afproj,t26_aff_1,t11_afproj,t59_aff_1,t33_aff_1,t11_afproj,t59_aff_1,t33_aff_1,t11_afproj,t59_aff_1,t33_aff_1]), [file(afproj,l57_afproj),interesting(0.00)]). fof(t37_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) & v1_aff_4(E,A) ) ) ) ) ) ), file(aff_4,t37_aff_4), [interesting(0.00)]). fof(t48_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) & v1_aff_4(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(C,B) ) ) ) ) ), file(aff_4,t48_aff_4), [interesting(0.00)]). fof(d14_incproj,definition,( ! [A] : ( ( v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ( v6_incproj(A) <=> ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r1_incsp_1(A,D,B) & r1_incsp_1(A,D,C) ) ) ) ) ) ), file(incproj,d14_incproj), [interesting(0.00)]). fof(t43_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(C,A) & v1_aff_4(D,A) & r2_hidden(B,C) & r2_hidden(B,D) & r1_aff_4(A,C,D) ) => r1_tarski(C,D) ) ) ) ) ) ), file(aff_4,t43_aff_4), [interesting(0.00)]). fof(d12_afproj,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m2_relset_1(B,k7_afproj(A),k8_afproj(A)) => ( B = k12_afproj(A) <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),B) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & C = k5_afproj(A,E) & D = k6_afproj(A,F) & v1_aff_1(E,A) & v1_aff_4(F,A) & r1_aff_4(A,E,F) ) ) ) ) ) ) ), file(afproj,d12_afproj), [interesting(0.00)]). fof(t13_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(B,A) & v1_aff_4(C,A) ) => ( k6_afproj(A,B) = k6_afproj(A,C) <=> r1_aff_4(A,B,C) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d6_afproj,t31_eqrel_1,t10_afproj,t58_aff_4,t10_afproj,t31_eqrel_1]), [file(afproj,t13_afproj),interesting(0.00)]). fof(t68_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(C,A) & v1_aff_4(D,A) & r1_aff_4(A,C,D) ) => r1_tarski(k2_aff_4(A,B,C),k3_aff_4(A,B,D)) ) ) ) ) ) ), file(aff_4,t68_aff_4), [interesting(0.00)]). fof(t66_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(C,A) => ( r2_hidden(B,C) <=> k3_aff_4(A,B,C) = C ) ) ) ) ) ), file(aff_4,t66_aff_4), [interesting(0.00)]). fof(t55_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(B,A) & v1_aff_4(C,A) ) => ( r1_aff_4(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & ? [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) & ~ r4_aff_1(A,D,E) & r1_tarski(D,B) & r1_tarski(E,B) & r1_tarski(F,C) & r1_tarski(G,C) & ( r4_aff_1(A,D,F) | r4_aff_1(A,F,D) ) & ( r4_aff_1(A,E,G) | r4_aff_1(A,G,E) ) ) ) ) ) ) ) ) ) ) ), file(aff_4,t55_aff_4), [interesting(0.00)]). fof(t5_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_aff_4(A,B,D) & r1_aff_4(A,B,E) & r1_aff_4(A,C,D) & r1_aff_4(A,C,E) & v1_aff_1(B,A) & v1_aff_1(C,A) & v1_aff_4(D,A) & v1_aff_4(E,A) ) => ( r4_aff_1(A,B,C) | r1_aff_4(A,D,E) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t59_aff_4,d3_tarski,t68_aff_4,t66_aff_4,d3_aff_4,t58_aff_1,t58_aff_1,t58_aff_1,t55_aff_4]), [file(afproj,t5_afproj),interesting(0.00)]). fof(t38_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k14_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k14_afproj(A))) => ~ ( r1_incsp_1(k14_afproj(A),B,D) & r1_incsp_1(k14_afproj(A),B,E) & r1_incsp_1(k14_afproj(A),C,D) & r1_incsp_1(k14_afproj(A),C,E) & B != C & D != E ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t21_afproj,t21_afproj,t24_afproj,t24_afproj,t11_afproj,t36_afproj,t5_afproj,t13_afproj]), [file(afproj,t38_afproj),interesting(0.00)]). fof(t40_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ? [D] : ( m1_subset_1(D,u2_incsp_1(k14_afproj(A))) & r1_incsp_1(k14_afproj(A),B,D) & r1_incsp_1(k14_afproj(A),C,D) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t21_afproj,t21_afproj,t31_aff_1,t27_aff_4,d3_aff_4,t38_aff_4,t24_afproj,t41_aff_4,t42_aff_4,t36_afproj]), [file(afproj,t40_afproj),interesting(0.00)]). fof(l55_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ( ~ ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) & ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k14_afproj(A))) => r1_incsp_1(k14_afproj(A),B,C) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t37_aff_4,t48_aff_4,t26_aff_1,d3_aff_1,t21_afproj,t24_afproj,t36_afproj,t43_aff_4]), [file(afproj,l55_afproj),interesting(0.00)]). fof(t39_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k14_afproj(A))) => ? [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) & ? [D] : ( m1_subset_1(D,u1_incsp_1(k14_afproj(A))) & ? [E] : ( m1_subset_1(E,u1_incsp_1(k14_afproj(A))) & r1_incsp_1(k14_afproj(A),C,B) & r1_incsp_1(k14_afproj(A),D,B) & r1_incsp_1(k14_afproj(A),E,B) & C != D & D != E & E != C ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t24_afproj,t34_aff_4,t16_aff_1,d3_aff_1,t21_afproj,t19_aff_4,t42_aff_4,t36_afproj,t26_aff_1,t11_afproj,t59_aff_1,t33_aff_1,t11_afproj,t59_aff_1,t33_aff_1,t11_afproj,t59_aff_1,t33_aff_1]), [file(afproj,t39_afproj),interesting(0.00)]). fof(t37_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k14_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( C = B & E = k4_tarski(D,2) ) => ( r1_incsp_1(k14_afproj(A),B,D) <=> r1_incsp_1(k13_afproj(A),C,E) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t21_afproj,t24_afproj,t36_afproj,t29_afproj,t29_afproj,t36_afproj]), [file(afproj,t37_afproj),interesting(0.00)]). fof(t30_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(D,A) & v1_aff_1(E,A) & r2_hidden(B,D) & r2_hidden(C,D) & r2_hidden(B,E) & r2_hidden(C,E) & B != C & D != E ) ) ) ) ) ) ), file(aff_1,t30_aff_1), [interesting(0.00)]). fof(l56_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),B,D) & r1_incsp_1(k13_afproj(A),B,E) & r1_incsp_1(k13_afproj(A),C,D) & r1_incsp_1(k13_afproj(A),C,E) & B != C & D != E ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t23_afproj,t23_afproj,t26_afproj,t27_afproj,t26_afproj,t27_afproj,t27_afproj,t30_aff_1,t27_afproj,t28_afproj,t27_afproj,t40_aff_4,t58_aff_1,t27_afproj,t59_aff_1,t20_afproj,t26_afproj,t27_afproj,t27_afproj,t28_afproj,t27_afproj,t40_aff_4,t58_aff_1,t27_afproj,t59_aff_1,t28_afproj,t40_aff_4,t58_aff_1,t11_afproj,t11_afproj,t29_afproj,t5_afproj,t13_afproj,t20_afproj,t20_afproj]), [file(afproj,l56_afproj),interesting(0.00)]). fof(t32_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != D & r2_hidden(D,C) ) ) ) ) ) ) ), file(aff_1,t32_aff_1), [interesting(0.00)]). fof(t39_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r4_aff_1(A,B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,D) & r1_tarski(C,D) & v1_aff_4(D,A) ) ) ) ) ) ) ), file(aff_4,t39_aff_4), [interesting(0.00)]). fof(t28_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(C,A) & v1_aff_1(D,A) & r2_hidden(B,C) & r1_tarski(D,C) ) => r1_tarski(k2_aff_4(A,B,D),C) ) ) ) ) ) ), file(aff_4,t28_aff_4), [interesting(0.00)]). fof(t50_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_aff_1(A,B,C) => ( v1_aff_1(B,A) & v1_aff_1(C,A) ) ) ) ) ) ), file(aff_1,t50_aff_1), [interesting(0.00)]). fof(t22_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(B,A) & v1_aff_1(C,A) & v1_aff_1(D,A) & r1_tarski(C,B) & r1_tarski(D,B) & ~ r4_aff_1(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r2_hidden(E,D) ) ) ) ) ) ) ) ), file(aff_4,t22_aff_4), [interesting(0.00)]). fof(t12_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(B,A) & v1_aff_1(C,A) ) => ( k5_afproj(A,B) = k5_afproj(A,C) <=> r1_aff_4(A,B,C) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t11_afproj,t40_aff_4]), [file(afproj,t12_afproj),interesting(0.00)]). fof(t71_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(D,A) & r2_hidden(B,D) & r2_hidden(C,D) ) => ( B = C | D = k2_aff_1(A,B,C) ) ) ) ) ) ) ), file(aff_1,t71_aff_1), [interesting(0.00)]). fof(l67_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),B,G) & r1_incsp_1(k13_afproj(A),C,G) & r1_incsp_1(k13_afproj(A),D,H) & r1_incsp_1(k13_afproj(A),E,H) & r1_incsp_1(k13_afproj(A),F,G) & r1_incsp_1(k13_afproj(A),F,H) & r1_incsp_1(k13_afproj(A),B,I) & r1_incsp_1(k13_afproj(A),D,I) & r1_incsp_1(k13_afproj(A),C,J) & r1_incsp_1(k13_afproj(A),E,J) & ~ r1_incsp_1(k13_afproj(A),F,I) & ~ r1_incsp_1(k13_afproj(A),F,J) & G != H & ~ m1_subset_1(F,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & ! [K] : ( m1_subset_1(K,u1_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),K,I) & r1_incsp_1(k13_afproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t20_afproj,l56_afproj,t23_afproj,t23_afproj,t23_afproj,t23_afproj,t26_afproj,t27_afproj,t27_afproj,t38_aff_4,t27_afproj,t42_aff_4,t27_afproj,t28_afproj,t27_afproj,t40_aff_4,t27_afproj,t59_aff_1,t27_afproj,t35_afproj,t26_afproj,t27_afproj,t28_afproj,t27_afproj,t40_aff_4,t58_aff_1,t34_afproj,t27_afproj,t28_afproj,t27_afproj,t40_aff_4,t58_aff_1,t26_afproj,t27_afproj,t27_afproj,d3_aff_4,t27_afproj,t28_aff_4,t58_aff_1,t27_afproj,t59_aff_1,t20_afproj,t27_afproj,t28_afproj,t27_afproj,t40_aff_4,t58_aff_1,t26_afproj,t27_afproj,t27_afproj,t71_aff_1,t19_aff_4,t27_afproj,t43_afproj,t29_afproj,t56_aff_4,t27_afproj,t27_afproj,t34_afproj,t27_afproj,t29_afproj,t5_afproj,t27_afproj,t27_afproj,t27_afproj,t34_afproj,t27_afproj,t29_afproj,t59_aff_4,t60_aff_4,t27_afproj,t43_aff_4,t27_afproj,t43_afproj]), [file(afproj,l67_afproj),interesting(0.00)]). fof(l68_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),B,G) & r1_incsp_1(k13_afproj(A),C,G) & r1_incsp_1(k13_afproj(A),D,H) & r1_incsp_1(k13_afproj(A),E,H) & r1_incsp_1(k13_afproj(A),F,G) & r1_incsp_1(k13_afproj(A),F,H) & r1_incsp_1(k13_afproj(A),B,I) & r1_incsp_1(k13_afproj(A),D,I) & r1_incsp_1(k13_afproj(A),C,J) & r1_incsp_1(k13_afproj(A),E,J) & ~ r1_incsp_1(k13_afproj(A),F,I) & ~ r1_incsp_1(k13_afproj(A),F,J) & G != H & ~ m1_subset_1(F,u1_struct_0(A)) & ~ ( ~ m1_subset_1(B,u1_struct_0(A)) & ~ m1_subset_1(C,u1_struct_0(A)) & ~ m1_subset_1(D,u1_struct_0(A)) & ~ m1_subset_1(E,u1_struct_0(A)) ) & ! [K] : ( m1_subset_1(K,u1_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),K,I) & r1_incsp_1(k13_afproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[l67_afproj,l67_afproj]), [file(afproj,l68_afproj),interesting(0.00)]). fof(l64_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u1_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u1_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ! [K] : ( m1_subset_1(K,u2_incsp_1(k13_afproj(A))) => ! [L] : ( m1_subset_1(L,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_1(C,A) & v1_aff_1(D,A) & v1_aff_4(E,A) & r1_tarski(C,E) & r1_tarski(D,E) & B = G & J = k4_tarski(C,1) & K = k4_tarski(D,1) & r1_incsp_1(k13_afproj(A),H,J) & r1_incsp_1(k13_afproj(A),I,K) & r1_incsp_1(k13_afproj(A),H,L) & r1_incsp_1(k13_afproj(A),I,L) & L = k4_tarski(k6_afproj(A,F),2) & v1_aff_4(F,A) ) => ( J = K | H = I | ( r1_aff_4(A,F,E) & r1_aff_4(A,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t20_afproj,t20_afproj,t27_afproj,t27_afproj,t11_afproj,t29_afproj,t42_aff_4,t28_afproj,t40_aff_4,t56_aff_4,t5_afproj]), [file(afproj,l64_afproj),interesting(0.00)]). fof(t6_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(B,A) & r1_aff_4(A,C,B) & r1_aff_4(A,B,D) ) => r1_aff_4(A,C,D) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t59_aff_4,t60_aff_4]), [file(afproj,t6_afproj),interesting(0.00)]). fof(t61_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(B,A) & v1_aff_4(C,A) & v1_aff_4(D,A) ) => ( ( ~ ( r1_aff_4(A,B,C) & r1_aff_4(A,C,D) ) & ~ ( r1_aff_4(A,B,C) & r1_aff_4(A,D,C) ) & ~ ( r1_aff_4(A,C,B) & r1_aff_4(A,C,D) ) & ~ ( r1_aff_4(A,C,B) & r1_aff_4(A,D,C) ) ) | ( r1_aff_4(A,B,D) & r1_aff_4(A,D,B) ) ) ) ) ) ) ) ), file(aff_4,t61_aff_4), [interesting(0.00)]). fof(l66_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),B,G) & r1_incsp_1(k13_afproj(A),C,G) & r1_incsp_1(k13_afproj(A),D,H) & r1_incsp_1(k13_afproj(A),E,H) & r1_incsp_1(k13_afproj(A),F,G) & r1_incsp_1(k13_afproj(A),F,H) & r1_incsp_1(k13_afproj(A),B,I) & r1_incsp_1(k13_afproj(A),D,I) & r1_incsp_1(k13_afproj(A),C,J) & r1_incsp_1(k13_afproj(A),E,J) & ~ r1_incsp_1(k13_afproj(A),F,I) & ~ r1_incsp_1(k13_afproj(A),F,J) & G != H & m1_subset_1(F,u1_struct_0(A)) & ! [K] : ( m1_subset_1(K,u1_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),K,I) & r1_incsp_1(k13_afproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[l56_afproj,t23_afproj,t23_afproj,t23_afproj,t23_afproj,t26_afproj,t27_afproj,t27_afproj,t38_aff_4,l63_afproj,t27_afproj,l63_afproj,t27_afproj,t43_afproj,l64_afproj,t27_afproj,t20_afproj,t30_afproj,t42_aff_4,t6_afproj,t29_afproj,l64_afproj,t27_afproj,l64_afproj,t27_afproj,t61_aff_4,l57_afproj,t13_afproj,l63_afproj,t27_afproj,t20_afproj,t42_aff_4,t6_afproj,t29_afproj,t30_afproj]), [file(afproj,l66_afproj),interesting(0.00)]). fof(l69_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),B,G) & r1_incsp_1(k13_afproj(A),C,G) & r1_incsp_1(k13_afproj(A),D,H) & r1_incsp_1(k13_afproj(A),E,H) & r1_incsp_1(k13_afproj(A),F,G) & r1_incsp_1(k13_afproj(A),F,H) & r1_incsp_1(k13_afproj(A),B,I) & r1_incsp_1(k13_afproj(A),D,I) & r1_incsp_1(k13_afproj(A),C,J) & r1_incsp_1(k13_afproj(A),E,J) & ~ r1_incsp_1(k13_afproj(A),F,I) & ~ r1_incsp_1(k13_afproj(A),F,J) & G != H & ! [K] : ( m1_subset_1(K,u1_incsp_1(k13_afproj(A))) => ~ ( r1_incsp_1(k13_afproj(A),K,I) & r1_incsp_1(k13_afproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t20_afproj,t20_afproj,t20_afproj,t20_afproj,t20_afproj,l56_afproj,t27_aff_4,d3_aff_4,t32_aff_1,t32_aff_1,t27_aff_4,d3_aff_4,t58_aff_1,t38_aff_4,t38_aff_4,t39_aff_4,t28_aff_4,t23_afproj,t32_afproj,l56_afproj,t23_afproj,t32_afproj,l56_afproj,t29_afproj,t56_aff_4,t43_aff_4,t58_aff_1,t58_aff_1,t58_aff_1,t11_afproj,t58_aff_1,t58_aff_1,t58_aff_1,t11_afproj,t22_aff_4,t22_aff_4,t11_afproj,t11_afproj,l56_afproj,t30_aff_1,t11_afproj,t30_aff_1,t11_afproj,t11_afproj,t11_afproj,t30_aff_1,t11_afproj,l56_afproj,d3_aff_1,t19_aff_4,t38_aff_4,t38_aff_4,t26_aff_1,t23_afproj,t32_afproj,l56_afproj,t19_aff_4,t20_afproj,t11_afproj,t31_afproj,t30_aff_1,d3_aff_1,t20_afproj,t19_aff_4,t31_afproj,t22_aff_4,l68_afproj,l66_afproj]), [file(afproj,l69_afproj),interesting(0.00)]). fof(t42_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k14_afproj(A))) => ( r2_hidden(k4_tarski(B,k4_tarski(C,2)),u3_incsp_1(k13_afproj(A))) => m1_subset_1(B,u1_incsp_1(k14_afproj(A))) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t25_afproj,t24_afproj,d1_incsp_1,t27_afproj,t20_afproj,t21_afproj]), [file(afproj,t42_afproj),interesting(0.00)]). fof(t44_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k14_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k14_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k14_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k14_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k14_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k14_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k14_afproj(A))) => ~ ( r1_incsp_1(k14_afproj(A),B,G) & r1_incsp_1(k14_afproj(A),C,G) & r1_incsp_1(k14_afproj(A),D,H) & r1_incsp_1(k14_afproj(A),E,H) & r1_incsp_1(k14_afproj(A),F,G) & r1_incsp_1(k14_afproj(A),F,H) & r1_incsp_1(k14_afproj(A),B,I) & r1_incsp_1(k14_afproj(A),D,I) & r1_incsp_1(k14_afproj(A),C,J) & r1_incsp_1(k14_afproj(A),E,J) & ~ r1_incsp_1(k14_afproj(A),F,I) & ~ r1_incsp_1(k14_afproj(A),F,J) & G != H & ! [K] : ( m1_subset_1(K,u1_incsp_1(k14_afproj(A))) => ~ ( r1_incsp_1(k14_afproj(A),K,I) & r1_incsp_1(k14_afproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t22_afproj,t25_afproj,t37_afproj,t7_mcart_1,t7_mcart_1,l69_afproj,d1_incsp_1,t42_afproj,t37_afproj]), [file(afproj,t44_afproj),interesting(0.00)]). fof(d9_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ( v1_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ~ ( r1_incsp_1(A,B,D) & r1_incsp_1(A,C,D) & r1_incsp_1(A,B,E) & r1_incsp_1(A,C,E) & B != C & D != E ) ) ) ) ) ) ) ), file(incproj,d9_incproj), [interesting(0.00)]). fof(d10_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ( v2_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r1_incsp_1(A,B,D) & r1_incsp_1(A,C,D) ) ) ) ) ) ), file(incproj,d10_incproj), [interesting(0.00)]). fof(d11_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ( v3_incproj(A) <=> ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => r1_incsp_1(A,B,C) ) ) ) ) ), file(incproj,d11_incproj), [interesting(0.00)]). fof(d12_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ( v4_incproj(A) <=> ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & C != D & D != E & E != C & r1_incsp_1(A,C,B) & r1_incsp_1(A,D,B) & r1_incsp_1(A,E,B) ) ) ) ) ) ) ), file(incproj,d12_incproj), [interesting(0.00)]). fof(d13_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ( v5_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ~ ( r1_incsp_1(A,B,H) & r1_incsp_1(A,C,H) & r1_incsp_1(A,D,I) & r1_incsp_1(A,E,I) & r1_incsp_1(A,F,H) & r1_incsp_1(A,F,I) & r1_incsp_1(A,B,J) & r1_incsp_1(A,D,J) & r1_incsp_1(A,C,K) & r1_incsp_1(A,E,K) & ~ r1_incsp_1(A,F,J) & ~ r1_incsp_1(A,F,K) & H != I & ! [L] : ( m1_subset_1(L,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,L,J) & r1_incsp_1(A,L,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(incproj,d13_incproj), [interesting(0.00)]). fof(t51_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_aff_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & D != E & F != G & r2_analoaf(A,D,E,F,G) & B = k2_aff_1(A,D,E) & C = k2_aff_1(A,F,G) ) ) ) ) ) ) ) ) ), file(aff_1,t51_aff_1), [interesting(0.00)]). fof(t14_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( B != C & ~ ( ~ ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,C,F,G) ) & ~ ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,F,G,B,C) ) & ~ ( r2_analoaf(A,D,E,B,C) & r2_analoaf(A,F,G,B,C) ) & ~ ( r2_analoaf(A,D,E,B,C) & r2_analoaf(A,B,C,F,G) ) ) & ~ r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ), file(aff_1,t14_aff_1), [interesting(0.00)]). fof(t9_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,G) & r2_hidden(B,H) & r2_hidden(C,G) & r2_hidden(D,G) & r2_hidden(E,H) & r2_hidden(F,H) & v1_aff_1(G,A) & v1_aff_1(H,A) & C = D ) => ( B = C | B = E | G = H | ( ~ r2_analoaf(A,C,E,D,F) & ~ r2_analoaf(A,E,C,F,D) ) | E = F ) ) ) ) ) ) ) ) ) ) ), file(aff_4,t9_aff_4), [interesting(0.00)]). fof(d6_incproj,definition,( ! [A,B,C,D] : ( r2_incproj(A,B,C,D) <=> ( A != B & B != C & C != A & D != A & D != B & D != C ) ) ), file(incproj,d6_incproj), [interesting(0.00)]). fof(d8_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ( r4_incproj(A,B,C,D,E) <=> ( r1_incsp_1(A,B,D) & r1_incsp_1(A,C,D) & r1_incsp_1(A,E,D) ) ) ) ) ) ) ) ), file(incproj,d8_incproj), [interesting(0.00)]). fof(d7_incproj,definition,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ( r3_incproj(A,B,C,D) <=> ( r1_incsp_1(A,B,D) & r1_incsp_1(A,C,D) ) ) ) ) ) ) ), file(incproj,d7_incproj), [interesting(0.00)]). fof(d20_incproj,definition,( ! [A] : ( ( v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ( v11_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u1_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ! [S] : ( m1_subset_1(S,u2_incsp_1(A)) => ! [T] : ( m1_subset_1(T,u2_incsp_1(A)) => ( ( r2_incproj(B,C,D,E) & r2_incproj(B,F,G,H) & r1_incsp_1(A,B,N) & r1_incsp_1(A,B,Q) & r4_incproj(A,D,H,L,I) & r4_incproj(A,E,F,O,J) & r4_incproj(A,C,G,R,K) & r4_incproj(A,C,H,M,J) & r4_incproj(A,E,G,P,I) & r4_incproj(A,D,F,S,K) & r4_incproj(A,F,G,N,H) & r4_incproj(A,C,D,Q,E) & r3_incproj(A,I,J,T) ) => ( N = Q | r1_incsp_1(A,K,T) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(incproj,d20_incproj), [interesting(0.00)]). fof(t53_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,F) & r2_hidden(C,F) & r2_hidden(D,G) & r2_hidden(E,G) & r3_aff_1(A,F,G) ) => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ), file(aff_1,t53_aff_1), [interesting(0.00)]). fof(t11_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_analoaf(A,B,C,C,B) & r2_analoaf(A,B,C,B,C) ) ) ) ) ), file(aff_1,t11_aff_1), [interesting(0.00)]). fof(t48_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( v1_aff_1(B,A) & v1_aff_1(C,A) & r2_hidden(D,B) & r2_hidden(D,C) & r2_hidden(E,B) & r2_hidden(F,B) & r2_hidden(G,B) & r2_hidden(H,C) & r2_hidden(I,C) & r2_hidden(J,C) & r2_analoaf(A,E,I,F,H) & r2_analoaf(A,F,J,G,I) ) => ( B = C | D = E | D = H | D = F | D = I | D = G | D = J | ( E != F & F != G & E != G ) | r2_analoaf(A,E,J,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t30_aff_1,t14_aff_1,t9_aff_4,t11_aff_1,t9_aff_4]), [file(afproj,t48_afproj),interesting(0.00)]). fof(d2_aff_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( v1_aff_1(B,A) & v1_aff_1(C,A) & r2_hidden(D,B) & r2_hidden(D,C) & r2_hidden(E,B) & r2_hidden(F,B) & r2_hidden(G,B) & r2_hidden(H,C) & r2_hidden(I,C) & r2_hidden(J,C) & r2_analoaf(A,E,I,F,H) & r2_analoaf(A,F,J,G,I) ) => ( B = C | D = E | D = H | D = F | D = I | D = G | D = J | r2_analoaf(A,E,J,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(aff_2,d2_aff_2), [interesting(0.00)]). fof(t4_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( B = u1_struct_0(A) & v1_aff_4(B,A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t48_aff_4]), [file(afproj,t4_afproj),interesting(0.00)]). fof(t8_aff_4,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,G) & r2_hidden(B,H) & r2_hidden(C,G) & r2_hidden(D,G) & r2_hidden(E,H) & r2_hidden(F,H) & v1_aff_1(G,A) & v1_aff_1(H,A) & B = D ) => ( B = C | B = E | G = H | ( ~ r2_analoaf(A,C,E,D,F) & ~ r2_analoaf(A,E,C,F,D) ) | B = F ) ) ) ) ) ) ) ) ) ) ), file(aff_4,t8_aff_4), [interesting(0.00)]). fof(d5_incproj,definition,( ! [A,B,C] : ( r1_incproj(A,B,C) <=> ( A != B & B != C & C != A ) ) ), file(incproj,d5_incproj), [interesting(0.00)]). fof(d19_incproj,definition,( ! [A] : ( ( v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ( v10_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u1_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ! [S] : ( m1_subset_1(S,u2_incsp_1(A)) => ! [T] : ( m1_subset_1(T,u2_incsp_1(A)) => ~ ( r4_incproj(A,B,C,L,D) & r4_incproj(A,B,F,M,E) & r4_incproj(A,B,H,N,G) & r4_incproj(A,H,F,O,K) & r4_incproj(A,H,I,P,D) & r4_incproj(A,F,J,Q,D) & r4_incproj(A,K,E,R,G) & r4_incproj(A,C,I,S,G) & r4_incproj(A,C,J,T,E) & r1_incproj(L,M,N) & B != D & B != F & B != H & B != C & B != E & B != G & D != C & F != E & H != G & ! [U] : ( m1_subset_1(U,u2_incsp_1(A)) => ~ r4_incproj(A,I,J,U,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(incproj,d19_incproj), [interesting(0.00)]). fof(t12_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,D) & r2_analoaf(A,D,D,B,C) ) ) ) ) ) ), file(aff_1,t12_aff_1), [interesting(0.00)]). fof(t50_afproj,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r2_hidden(E,B) & r2_hidden(E,C) & r2_hidden(E,D) & r2_hidden(F,B) & r2_hidden(I,B) & r2_hidden(G,C) & r2_hidden(J,C) & r2_hidden(H,D) & r2_hidden(K,D) & v1_aff_1(B,A) & v1_aff_1(C,A) & v1_aff_1(D,A) & r2_analoaf(A,F,G,I,J) & r2_analoaf(A,F,H,I,K) ) => ( E = F | E = G | E = H | B = C | B = D | ( E != I & F != I ) | r2_analoaf(A,G,H,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t8_aff_4,t8_aff_4,t12_aff_1,t9_aff_4,t9_aff_4,t11_aff_1]), [file(afproj,t50_afproj),interesting(0.00)]). fof(t65_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(F,A) & r2_hidden(B,F) & r2_hidden(C,F) & r2_hidden(D,F) & r2_hidden(E,F) ) => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ), file(aff_1,t65_aff_1), [interesting(0.00)]). fof(d4_aff_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r2_hidden(E,B) & r2_hidden(E,C) & r2_hidden(E,D) & r2_hidden(F,B) & r2_hidden(I,B) & r2_hidden(G,C) & r2_hidden(J,C) & r2_hidden(H,D) & r2_hidden(K,D) & v1_aff_1(B,A) & v1_aff_1(C,A) & v1_aff_1(D,A) & r2_analoaf(A,F,G,I,J) & r2_analoaf(A,F,H,I,K) ) => ( E = F | E = G | E = H | B = C | B = D | r2_analoaf(A,G,H,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(aff_2,d4_aff_2), [interesting(0.00)]). fof(d2_aff_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k1_aff_1(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,D) <=> r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) ), file(aff_1,d2_aff_1), [interesting(0.00)]). fof(d1_aff_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ), file(aff_1,d1_aff_1), [interesting(0.00)]). fof(t15_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) => ( r1_aff_1(A,B,D,C) & r1_aff_1(A,C,B,D) & r1_aff_1(A,C,D,B) & r1_aff_1(A,D,B,C) & r1_aff_1(A,D,C,B) ) ) ) ) ) ) ), file(aff_1,t15_aff_1), [interesting(0.00)]). fof(t13_aff_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => ( r2_analoaf(A,B,C,E,D) & r2_analoaf(A,C,B,D,E) & r2_analoaf(A,C,B,E,D) & r2_analoaf(A,D,E,B,C) & r2_analoaf(A,D,E,C,B) & r2_analoaf(A,E,D,B,C) & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ), file(aff_1,t13_aff_1), [interesting(0.00)]). fof(d18_incproj,definition,( ! [A] : ( ( v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ( v9_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ~ ( ~ r1_incsp_1(A,C,I) & ~ r1_incsp_1(A,D,I) & ~ r1_incsp_1(A,B,J) & ~ r1_incsp_1(A,E,J) & ~ r1_incsp_1(A,B,K) & ~ r1_incsp_1(A,D,K) & ~ r1_incsp_1(A,C,L) & ~ r1_incsp_1(A,E,L) & r4_incproj(A,F,B,I,E) & r4_incproj(A,F,C,J,D) & r4_incproj(A,G,C,K,E) & r4_incproj(A,G,B,L,D) & r4_incproj(A,H,B,M,C) & r4_incproj(A,H,D,N,E) & r3_incproj(A,F,G,O) & r1_incsp_1(A,H,O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(incproj,d18_incproj), [interesting(0.00)]). fof(d5_papdesaf,definition,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v1_translac(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) & r2_analoaf(A,B,E,C,D) ) => r2_analoaf(A,B,C,B,D) ) ) ) ) ) ) ) ), file(papdesaf,d5_papdesaf), [interesting(0.00)]).