%   ORIGINAL: 'h4/thm/hreal/HRAT_LT_LADD_'
% 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: !x y z. 'h4/const/hreal/hrat_lt' ('h4/const/hrat/hrat_add' z x) ('h4/const/hrat/hrat_add' z y) <=> 'h4/const/hreal/hrat_lt' x y
%   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: !x y z. 'h4/const/hreal/hrat_lt' ('h4/const/hrat/hrat_add' z x) ('h4/const/hrat/hrat_add' z y) <=> 'h4/const/hreal/hrat_lt' x y
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_3f36229,V_3f36225]: ![F, G]: (![X]: s(V_3f36225,happ(s(fun(V_3f36229,V_3f36225),F),s(V_3f36229,X))) = s(V_3f36225,happ(s(fun(V_3f36229,V_3f36225),G),s(V_3f36229,X))) => s(fun(V_3f36229,V_3f36225),F) = s(fun(V_3f36229,V_3f36225),G))).
fof('h4/thm/hreal/HRAT_LT_LADD_', conjecture, ![X, Y, Z]: s(bool,'h4/const/hreal/hrat_lt'(s('h4/type/hrat/hrat','h4/const/hrat/hrat_add'(s('h4/type/hrat/hrat',Z),s('h4/type/hrat/hrat',X))),s('h4/type/hrat/hrat','h4/const/hrat/hrat_add'(s('h4/type/hrat/hrat',Z),s('h4/type/hrat/hrat',Y))))) = s(bool,'h4/const/hreal/hrat_lt'(s('h4/type/hrat/hrat',X),s('h4/type/hrat/hrat',Y)))).
