%   ORIGINAL: 'h4/thm/bool/ABS_REP_THM_'
% 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: !P. (?rep. 'h4/const/bool/TYPE_DEFINITION' P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
%   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: !P. (?rep. 'h4/const/bool/TYPE_DEFINITION' P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
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_3f34203,V_3f34199]: ![F, G]: (![X]: s(V_3f34199,happ(s(fun(V_3f34203,V_3f34199),F),s(V_3f34203,X))) = s(V_3f34199,happ(s(fun(V_3f34203,V_3f34199),G),s(V_3f34203,X))) => s(fun(V_3f34203,V_3f34199),F) = s(fun(V_3f34203,V_3f34199),G))).
fof('h4/thm/bool/ABS_REP_THM_', conjecture, ![B,A]: ![P]: (?[Rep]: p(s(bool,'h4/const/bool/TYPE_DEFINITION'(s(fun(A,bool),P),s(fun(B,A),Rep)))) => ?[Rep, Abs]: (![A0]: s(B,happ(s(fun(A,B),Abs),s(A,happ(s(fun(B,A),Rep),s(B,A0))))) = s(B,A0) & ![R]: (p(s(bool,happ(s(fun(A,bool),P),s(A,R)))) <=> s(A,happ(s(fun(B,A),Rep),s(B,happ(s(fun(A,B),Abs),s(A,R))))) = s(A,R))))).
