%   ORIGINAL: 'h4/thm/quotient/CONJ_IMPLIES_'
% 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 ==> Q) /\ ('P\'' ==> 'Q\'') ==> P /\ 'P\'' ==> Q /\ '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 ==> Q) /\ ('P\'' ==> 'Q\'') ==> P /\ 'P\'' ==> Q /\ '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_3f76065,V_3f76061]: ![F, G]: (![X]: s(V_3f76061,happ(s(fun(V_3f76065,V_3f76061),F),s(V_3f76065,X))) = s(V_3f76061,happ(s(fun(V_3f76065,V_3f76061),G),s(V_3f76065,X))) => s(fun(V_3f76065,V_3f76061),F) = s(fun(V_3f76065,V_3f76061),G))).
fof('h4/thm/quotient/CONJ_IMPLIES_', conjecture, ![P, V_27P_5c_27_27, Q, 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)))) => ((p(s(bool,P)) & p(s(bool,V_27P_5c_27_27))) => (p(s(bool,Q)) & p(s(bool,V_27Q_5c_27_27)))))).
