%   ORIGINAL: 'h4/thm/bool/PULL_FORALL_1'
% 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: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
%   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: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
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_3f35779,V_3f35775]: ![F, G]: (![X]: s(V_3f35775,happ(s(fun(V_3f35779,V_3f35775),F),s(V_3f35779,X))) = s(V_3f35775,happ(s(fun(V_3f35779,V_3f35775),G),s(V_3f35779,X))) => s(fun(V_3f35779,V_3f35775),F) = s(fun(V_3f35779,V_3f35775),G))).
fof('h4/thm/bool/PULL_FORALL_1', conjecture, ![A]: ![Q, P]: ((![X]: p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) & p(s(bool,Q))) <=> ![X]: (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) & p(s(bool,Q))))).
