%   ORIGINAL: h4/arithmetic/LESS__MONO__REV
% 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/prim__rec/SUC__LESS: !n m. h4/prim__rec/_3C (h4/num/SUC m) n ==> h4/prim__rec/_3C m n
% Assm: h4/prim__rec/LESS__THM: !n m. h4/prim__rec/_3C m (h4/num/SUC n) <=> m = n \/ h4/prim__rec/_3C m n
% Assm: h4/prim__rec/EQ__LESS: !n m. h4/num/SUC m = n ==> h4/prim__rec/_3C m n
% Goal: !n m. h4/prim__rec/_3C (h4/num/SUC m) (h4/num/SUC n) ==> h4/prim__rec/_3C 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_primu_u_recs_SUCu_u_LESS]: !n m. h4/prim__rec/_3C (h4/num/SUC m) n ==> h4/prim__rec/_3C m n
% Assm [h4s_primu_u_recs_LESSu_u_THM]: !n m. h4/prim__rec/_3C m (h4/num/SUC n) <=> m = n \/ h4/prim__rec/_3C m n
% Assm [h4s_primu_u_recs_EQu_u_LESS]: !n m. h4/num/SUC m = n ==> h4/prim__rec/_3C m n
% Goal: !n m. h4/prim__rec/_3C (h4/num/SUC m) (h4/num/SUC n) ==> h4/prim__rec/_3C 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_Q305273,TV_Q305269]: ![V_f, V_g]: (![V_x]: s(TV_Q305269,happ(s(t_fun(TV_Q305273,TV_Q305269),V_f),s(TV_Q305273,V_x))) = s(TV_Q305269,happ(s(t_fun(TV_Q305273,TV_Q305269),V_g),s(TV_Q305273,V_x))) => s(t_fun(TV_Q305273,TV_Q305269),V_f) = s(t_fun(TV_Q305273,TV_Q305269),V_g))).
fof(ah4s_primu_u_recs_SUCu_u_LESS, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(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)))))).
fof(ah4s_primu_u_recs_LESSu_u_THM, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))) <=> (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))))))).
fof(ah4s_primu_u_recs_EQu_u_LESS, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_nums_suc(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)))))).
fof(ch4s_arithmetics_LESSu_u_MONOu_u_REV, conjecture, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_suc(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)))))).
