%   ORIGINAL: 'h4/thm/bool/bool_case_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 Q x 'x\'' y 'y\''. (P <=> Q) /\ (Q ==> x = 'x\'') /\ (~Q ==> y = 'y\'') ==> 'h4/const/bool/COND' P x y = 'h4/const/bool/COND' Q 'x\'' 'y\''
%   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 Q x 'x\'' y 'y\''. (P <=> Q) /\ (Q ==> x = 'x\'') /\ (~Q ==> y = 'y\'') ==> 'h4/const/bool/COND' P x y = 'h4/const/bool/COND' Q 'x\'' 'y\''
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_3f35078,V_3f35074]: ![F, G]: (![X]: s(V_3f35074,happ(s(fun(V_3f35078,V_3f35074),F),s(V_3f35078,X))) = s(V_3f35074,happ(s(fun(V_3f35078,V_3f35074),G),s(V_3f35078,X))) => s(fun(V_3f35078,V_3f35074),F) = s(fun(V_3f35078,V_3f35074),G))).
fof('h4/thm/bool/bool_case_CONG_', conjecture, ![A]: ![P, Q, X, V_27x_5c_27_27, Y, V_27y_5c_27_27]: ((s(bool,P) = s(bool,Q) & ((p(s(bool,Q)) => s(A,X) = s(A,V_27x_5c_27_27)) & (~ (p(s(bool,Q))) => s(A,Y) = s(A,V_27y_5c_27_27)))) => s(A,'h4/const/bool/COND'(s(bool,P),s(A,X),s(A,Y))) = s(A,'h4/const/bool/COND'(s(bool,Q),s(A,V_27x_5c_27_27),s(A,V_27y_5c_27_27))))).
