%   ORIGINAL: 'h4/thm/list/EXISTS_SNOC_'
% 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 x l. 'h4/const/list/EXISTS' P ('h4/const/list/SNOC' x l) <=> P x \/ 'h4/const/list/EXISTS' P l
%   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 x l. 'h4/const/list/EXISTS' P ('h4/const/list/SNOC' x l) <=> happ P x \/ 'h4/const/list/EXISTS' P l
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_3f8891,V_3f8887]: ![F, G]: (![X]: s(V_3f8887,happ(s(fun(V_3f8891,V_3f8887),F),s(V_3f8891,X))) = s(V_3f8887,happ(s(fun(V_3f8891,V_3f8887),G),s(V_3f8891,X))) => s(fun(V_3f8891,V_3f8887),F) = s(fun(V_3f8891,V_3f8887),G))).
fof('h4/thm/list/EXISTS_SNOC_', conjecture, ![A]: ![P, X, L]: (p(s(bool,'h4/const/list/EXISTS'(s(fun(A,bool),P),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),L)))))) <=> (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) | p(s(bool,'h4/const/list/EXISTS'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))))))).
