%   ORIGINAL: 'h4/thm/list/EVERY_SIMP_'
% 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: !c l. 'h4/const/list/EVERY' (\x. c) l <=> l = 'h4/const/list/NIL' \/ c
%   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: !_0. (!c x. happ (happ _0 c) x <=> c) ==> (!c l. 'h4/const/list/EVERY' (happ _0 c) l <=> l = 'h4/const/list/NIL' \/ c)
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_3f3563,V_3f3559]: ![F, G]: (![X]: s(V_3f3559,happ(s(fun(V_3f3563,V_3f3559),F),s(V_3f3563,X))) = s(V_3f3559,happ(s(fun(V_3f3563,V_3f3559),G),s(V_3f3563,X))) => s(fun(V_3f3563,V_3f3559),F) = s(fun(V_3f3563,V_3f3559),G))).
fof('h4/thm/list/EVERY_SIMP_', conjecture, ![A]: ![V__0]: (![C, X]: s(bool,happ(s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),V__0),s(bool,C))),s(A,X))) = s(bool,C) => ![C, L]: (p(s(bool,'h4/const/list/EVERY'(s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),V__0),s(bool,C))),s('h4/type/list/list'(A),L)))) <=> (s('h4/type/list/list'(A),L) = s('h4/type/list/list'(A),'h4/const/list/NIL') | p(s(bool,C)))))).
