%   ORIGINAL: 'h4/thm/bool/TYPE_DEFINITION_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 <=> (!'x\'' 'x\'\''. rep 'x\'' = rep 'x\'\'' ==> 'x\'' = 'x\'\'') /\ (!x. P x <=> (?'x\''. x = rep 'x\''))
%   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 <=> (!'x\'' 'x\'\''. happ rep 'x\'' = happ rep 'x\'\'' ==> 'x\'' = 'x\'\'') /\ (!x. happ P x <=> (?'x\''. x = happ rep 'x\''))
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_3f34128,V_3f34124]: ![F, G]: (![X]: s(V_3f34124,happ(s(fun(V_3f34128,V_3f34124),F),s(V_3f34128,X))) = s(V_3f34124,happ(s(fun(V_3f34128,V_3f34124),G),s(V_3f34128,X))) => s(fun(V_3f34128,V_3f34124),F) = s(fun(V_3f34128,V_3f34124),G))).
fof('h4/thm/bool/TYPE_DEFINITION_THM_', conjecture, ![A,B]: ![P, Rep]: (p(s(bool,'h4/const/bool/TYPE_DEFINITION'(s(fun(A,bool),P),s(fun(B,A),Rep)))) <=> (![V_27x_5c_27_27, V_27x_5c_27_5c_27_27]: (s(A,happ(s(fun(B,A),Rep),s(B,V_27x_5c_27_27))) = s(A,happ(s(fun(B,A),Rep),s(B,V_27x_5c_27_5c_27_27))) => s(B,V_27x_5c_27_27) = s(B,V_27x_5c_27_5c_27_27)) & ![X]: (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) <=> ?[V_27x_5c_27_27]: s(A,X) = s(A,happ(s(fun(B,A),Rep),s(B,V_27x_5c_27_27))))))).
