%   ORIGINAL: h4/numpair/tri__LE
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/LESS__OR__EQ: !n m. h4/arithmetic/_3C_3D m n <=> h4/prim__rec/_3C m n \/ m = n
% Assm: h4/numpair/tri__LT: !n m. h4/prim__rec/_3C (h4/numpair/tri n) (h4/numpair/tri m) <=> h4/prim__rec/_3C n m
% Assm: h4/numpair/tri__11: !n m. h4/numpair/tri m = h4/numpair/tri n <=> m = n
% Goal: !n m. h4/arithmetic/_3C_3D (h4/numpair/tri m) (h4/numpair/tri n) <=> h4/arithmetic/_3C_3D m n
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_LESSu_u_ORu_u_EQ]: !n m. h4/arithmetic/_3C_3D m n <=> h4/prim__rec/_3C m n \/ m = n
% Assm [h4s_numpairs_triu_u_LT]: !n m. h4/prim__rec/_3C (h4/numpair/tri n) (h4/numpair/tri m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numpairs_triu_u_11]: !n m. h4/numpair/tri m = h4/numpair/tri n <=> m = n
% Goal: !n m. h4/arithmetic/_3C_3D (h4/numpair/tri m) (h4/numpair/tri n) <=> h4/arithmetic/_3C_3D m n
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q144260,TV_Q144256]: ![V_f, V_g]: (![V_x]: s(TV_Q144256,happ(s(t_fun(TV_Q144260,TV_Q144256),V_f),s(TV_Q144260,V_x))) = s(TV_Q144256,happ(s(t_fun(TV_Q144260,TV_Q144256),V_g),s(TV_Q144260,V_x))) => s(t_fun(TV_Q144260,TV_Q144256),V_f) = s(t_fun(TV_Q144260,TV_Q144256),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_arithmetics_LESSu_u_ORu_u_EQ, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) | s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)))).
fof(ah4s_numpairs_triu_u_LT, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numpairs_triu_u_11, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ch4s_numpairs_triu_u_LE, conjecture, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
