%   ORIGINAL: 'h4/thm/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
% Goal: !h i. 'h4/const/hreal/hreal_lt' h i ==> 'h4/const/realax/treal_lt' ('h4/const/realax/treal_of_hreal' h) ('h4/const/realax/treal_of_hreal' i)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !h i. 'h4/const/hreal/hreal_lt' h i ==> 'h4/const/realax/treal_lt' ('h4/const/realax/treal_of_hreal' h) ('h4/const/realax/treal_of_hreal' i)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f49611,V_3f49607]: ![F, G]: (![X]: s(V_3f49607,happ(s(fun(V_3f49611,V_3f49607),F),s(V_3f49611,X))) = s(V_3f49607,happ(s(fun(V_3f49611,V_3f49607),G),s(V_3f49611,X))) => s(fun(V_3f49611,V_3f49607),F) = s(fun(V_3f49611,V_3f49607),G))).
fof('h4/thm/realax/TREAL_ISO_', conjecture, ![H, I]: (p(s(bool,'h4/const/hreal/hreal_lt'(s('h4/type/hreal/hreal',H),s('h4/type/hreal/hreal',I)))) => p(s(bool,'h4/const/realax/treal_lt'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),'h4/const/realax/treal_of_hreal'(s('h4/type/hreal/hreal',H))),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),'h4/const/realax/treal_of_hreal'(s('h4/type/hreal/hreal',I)))))))).
