%   ORIGINAL: 'h4/thm/hrat/hrat_ABS_REP_CLASS_e1'
% 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: !c. (?r. 'h4/const/hrat/trat_eq' r r /\ c = 'h4/const/hrat/trat_eq' r) <=> 'h4/const/hrat/hrat_REP_CLASS' ('h4/const/hrat/hrat_ABS_CLASS' c) = c
%   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: !c. (?r. happ ('h4/const/hrat/trat_eq' r) r /\ c = 'h4/const/hrat/trat_eq' r) <=> 'h4/const/hrat/hrat_REP_CLASS' ('h4/const/hrat/hrat_ABS_CLASS' c) = c
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_3f13819,V_3f13815]: ![F, G]: (![X]: s(V_3f13815,happ(s(fun(V_3f13819,V_3f13815),F),s(V_3f13819,X))) = s(V_3f13815,happ(s(fun(V_3f13819,V_3f13815),G),s(V_3f13819,X))) => s(fun(V_3f13819,V_3f13815),F) = s(fun(V_3f13819,V_3f13815),G))).
fof('h4/thm/hrat/hrat_ABS_REP_CLASS_e1', conjecture, ![C]: (?[R]: (p(s(bool,happ(s(fun('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),bool),'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),R))),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),R)))) & s(fun('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),bool),C) = s(fun('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),bool),'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),R)))) <=> s(fun('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),bool),'h4/const/hrat/hrat_REP_CLASS'(s('h4/type/hrat/hrat','h4/const/hrat/hrat_ABS_CLASS'(s(fun('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),bool),C))))) = s(fun('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),bool),C))).
