%   ORIGINAL: 'h4/thm/bool/MONO_COND_'
% 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: !z y x w b. (x ==> y) ==> (z ==> w) ==> 'h4/const/bool/COND' b x z ==> 'h4/const/bool/COND' b y w
%   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: !z y x w b. (x ==> y) ==> (z ==> w) ==> 'h4/const/bool/COND' b x z ==> 'h4/const/bool/COND' b y w
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_3f34753,V_3f34749]: ![F, G]: (![X]: s(V_3f34749,happ(s(fun(V_3f34753,V_3f34749),F),s(V_3f34753,X))) = s(V_3f34749,happ(s(fun(V_3f34753,V_3f34749),G),s(V_3f34753,X))) => s(fun(V_3f34753,V_3f34749),F) = s(fun(V_3f34753,V_3f34749),G))).
fof('h4/thm/bool/MONO_COND_', conjecture, ![Z, Y, X, W, B]: ((p(s(bool,X)) => p(s(bool,Y))) => ((p(s(bool,Z)) => p(s(bool,W))) => (p(s(bool,'h4/const/bool/COND'(s(bool,B),s(bool,X),s(bool,Z)))) => p(s(bool,'h4/const/bool/COND'(s(bool,B),s(bool,Y),s(bool,W)))))))).
