%   ORIGINAL: h4/realax/TREAL__ISO
% 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/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/hreal/HREAL__ADD__SYM: !Y X. h4/hreal/hreal__add X Y = h4/hreal/hreal__add Y X
% Assm: h4/hreal/HREAL__ADD__ASSOC: !Z Y X. h4/hreal/hreal__add X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__add X Y) Z
% Assm: h4/realax/HREAL__LT__LADD: !z y x. h4/hreal/hreal__lt (h4/hreal/hreal__add x y) (h4/hreal/hreal__add x z) <=> h4/hreal/hreal__lt y z
% Assm: h4/realax/treal__lt0: !y2 y1 x2 x1. h4/realax/treal__lt (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) <=> h4/hreal/hreal__lt (h4/hreal/hreal__add x1 y2) (h4/hreal/hreal__add x2 y1)
% Assm: h4/realax/treal__of__hreal0: !x. h4/realax/treal__of__hreal x = h4/pair/_2C (h4/hreal/hreal__add x h4/hreal/hreal__1) h4/hreal/hreal__1
% Goal: !i h. h4/hreal/hreal__lt h i ==> h4/realax/treal__lt (h4/realax/treal__of__hreal h) (h4/realax/treal__of__hreal i)
%   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_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_hreals_HREALu_u_ADDu_u_SYM]: !Y X. h4/hreal/hreal__add X Y = h4/hreal/hreal__add Y X
% Assm [h4s_hreals_HREALu_u_ADDu_u_ASSOC]: !Z Y X. h4/hreal/hreal__add X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__add X Y) Z
% Assm [h4s_realaxs_HREALu_u_LTu_u_LADD]: !z y x. h4/hreal/hreal__lt (h4/hreal/hreal__add x y) (h4/hreal/hreal__add x z) <=> h4/hreal/hreal__lt y z
% Assm [h4s_realaxs_trealu_u_lt0]: !y2 y1 x2 x1. h4/realax/treal__lt (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) <=> h4/hreal/hreal__lt (h4/hreal/hreal__add x1 y2) (h4/hreal/hreal__add x2 y1)
% Assm [h4s_realaxs_trealu_u_ofu_u_hreal0]: !x. h4/realax/treal__of__hreal x = h4/pair/_2C (h4/hreal/hreal__add x h4/hreal/hreal__1) h4/hreal/hreal__1
% Goal: !i h. h4/hreal/hreal__lt h i ==> h4/realax/treal__lt (h4/realax/treal__of__hreal h) (h4/realax/treal__of__hreal i)
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_Q328966,TV_Q328962]: ![V_f, V_g]: (![V_x]: s(TV_Q328962,happ(s(t_fun(TV_Q328966,TV_Q328962),V_f),s(TV_Q328966,V_x))) = s(TV_Q328962,happ(s(t_fun(TV_Q328966,TV_Q328962),V_g),s(TV_Q328966,V_x))) => s(t_fun(TV_Q328966,TV_Q328962),V_f) = s(t_fun(TV_Q328966,TV_Q328962),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_hreals_HREALu_u_ADDu_u_SYM, axiom, ![V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_X)))).
fof(ah4s_hreals_HREALu_u_ADDu_u_ASSOC, axiom, ![V_Z, V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_Z))))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hreals_hreal,V_Z)))).
fof(ah4s_realaxs_HREALu_u_LTu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_z))))) = s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_z)))).
fof(ah4s_realaxs_trealu_u_lt0, axiom, ![V_y2, V_y1, V_x2, V_x1]: s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y2))))) = s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y2))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y1)))))).
fof(ah4s_realaxs_trealu_u_ofu_u_hreal0, axiom, ![V_x]: s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,V_x))) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)))).
fof(ch4s_realaxs_TREALu_u_ISO, conjecture, ![V_i, V_h]: (p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_h),s(t_h4s_hreals_hreal,V_i)))) => p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,V_h))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,V_i)))))))).
