%   ORIGINAL: 'h4/thm/relation/INVOL_'
% 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: !f. 'h4/const/relation/INVOL' f <=> (!x. f (f x) = 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: !f. 'h4/const/relation/INVOL' f <=> (!x. happ f (happ f x) = 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_3f29153,V_3f29149]: ![F, G]: (![X]: s(V_3f29149,happ(s(fun(V_3f29153,V_3f29149),F),s(V_3f29153,X))) = s(V_3f29149,happ(s(fun(V_3f29153,V_3f29149),G),s(V_3f29153,X))) => s(fun(V_3f29153,V_3f29149),F) = s(fun(V_3f29153,V_3f29149),G))).
fof('h4/thm/relation/INVOL_', conjecture, ![Z]: ![F]: (p(s(bool,'h4/const/relation/INVOL'(s(fun(Z,Z),F)))) <=> ![X]: s(Z,happ(s(fun(Z,Z),F),s(Z,happ(s(fun(Z,Z),F),s(Z,X))))) = s(Z,X))).
