%   ORIGINAL: 'h4/thm/bool/LEFT_AND_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: !P 'P\'' Q 'Q\''. (P <=> 'P\'') /\ ('P\'' ==> (Q <=> 'Q\'')) ==> (P /\ Q <=> 'P\'' /\ '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: !P 'P\'' Q 'Q\''. (P <=> 'P\'') /\ ('P\'' ==> (Q <=> 'Q\'')) ==> (P /\ Q <=> 'P\'' /\ '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_3f34428,V_3f34424]: ![F, G]: (![X]: s(V_3f34424,happ(s(fun(V_3f34428,V_3f34424),F),s(V_3f34428,X))) = s(V_3f34424,happ(s(fun(V_3f34428,V_3f34424),G),s(V_3f34428,X))) => s(fun(V_3f34428,V_3f34424),F) = s(fun(V_3f34428,V_3f34424),G))).
fof('h4/thm/bool/LEFT_AND_CONG_', conjecture, ![P, V_27P_5c_27_27, Q, V_27Q_5c_27_27]: ((s(bool,P) = s(bool,V_27P_5c_27_27) & (p(s(bool,V_27P_5c_27_27)) => s(bool,Q) = s(bool,V_27Q_5c_27_27))) => ((p(s(bool,P)) & p(s(bool,Q))) <=> (p(s(bool,V_27P_5c_27_27)) & p(s(bool,V_27Q_5c_27_27)))))).
