fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,![A_27b, A_27c]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Efinite__map_2EFDOM_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))))).
fof(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27b_2CA_27a_29,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Efinite__map_2EFDOM_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),X0_2E0))))).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(A_27c,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0),s(A_27b,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Efinite__map_2EFAPPLY_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))),s(A_27b,X1_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27b_2CA_27a_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a))),c_2Efinite__map_2EFAPPLY_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),X0_2E0))),s(A_27b,X1_2E0))))).
fof(arityeq3_2Ec_2Efmaptree_2Erelrec_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2Efmaptree_2Erelrec_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c))),X0_2E0),s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),X1_2E0),s(A_27c,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c))),tyop_2Emin_2Efun(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Efmaptree_2Erelrec_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c))),X0_2E0))),s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),X1_2E0))),s(A_27c,X2_2E0))))).
fof(arityeq2_2Ec_2Efmaptree_2EFTNode_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),c_2Efmaptree_2EFTNode_2E2(s(A_27a,X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),X1_2E0))) = s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),tyop_2Efmaptree_2Efmaptree(A_27b,A_27a))),c_2Efmaptree_2EFTNode_2E0),s(A_27a,X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),X1_2E0))))).
fof(fmaptreeTheory_2Erelrec__rules,axiom,![A_27a, A_27b, A_27c]: ![V0h_2E0, V1i_2E0, V2fm_2E0, V3rfm_2E0]: (((s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3rfm_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),V2fm_2E0)))) & ![V4d_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),V2fm_2E0)))))) => p(s(tyop_2Emin_2Ebool,c_2Efmaptree_2Erelrec_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c))),V0h_2E0),s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),V2fm_2E0),s(A_27b,V4d_2E0))),s(A_27c,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3rfm_2E0),s(A_27b,V4d_2E0)))))))) => p(s(tyop_2Emin_2Ebool,c_2Efmaptree_2Erelrec_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c))),V0h_2E0),s(tyop_2Efmaptree_2Efmaptree(A_27b,A_27a),c_2Efmaptree_2EFTNode_2E2(s(A_27a,V1i_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),V2fm_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),A_27c))),V0h_2E0),s(A_27a,V1i_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3rfm_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Efmaptree_2Efmaptree(A_27b,A_27a)),V2fm_2E0)))))))).
