%   ORIGINAL: 'h4/thm/bool/RES_FORALL_CONG_'
% 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: !g f Q P. P = Q ==> (!x. 'h4/const/bool/IN' x Q ==> (f x <=> g x)) ==> ('h4/const/bool/RES_FORALL' P f <=> 'h4/const/bool/RES_FORALL' Q g)
%   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: !g f Q P. P = Q ==> (!x. 'h4/const/bool/IN' x Q ==> (happ f x <=> happ g x)) ==> ('h4/const/bool/RES_FORALL' P f <=> 'h4/const/bool/RES_FORALL' Q g)
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_3f34528,V_3f34524]: ![F, G]: (![X]: s(V_3f34524,happ(s(fun(V_3f34528,V_3f34524),F),s(V_3f34528,X))) = s(V_3f34524,happ(s(fun(V_3f34528,V_3f34524),G),s(V_3f34528,X))) => s(fun(V_3f34528,V_3f34524),F) = s(fun(V_3f34528,V_3f34524),G))).
fof('h4/thm/bool/RES_FORALL_CONG_', conjecture, ![A]: ![G, F, Q, P]: (s(fun(A,bool),P) = s(fun(A,bool),Q) => (![X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),Q)))) => s(bool,happ(s(fun(A,bool),F),s(A,X))) = s(bool,happ(s(fun(A,bool),G),s(A,X)))) => s(bool,'h4/const/bool/RES_FORALL'(s(fun(A,bool),P),s(fun(A,bool),F))) = s(bool,'h4/const/bool/RES_FORALL'(s(fun(A,bool),Q),s(fun(A,bool),G)))))).
