%   ORIGINAL: 'h4/thm/list/EVERY_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: !l1 l2 P 'P\''. l1 = l2 /\ (!x. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' l2) ==> (P x <=> 'P\'' x)) ==> ('h4/const/list/EVERY' P l1 <=> 'h4/const/list/EVERY' 'P\'' l2)
%   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: !l1 l2 P 'P\''. l1 = l2 /\ (!x. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' l2) ==> (happ P x <=> happ 'P\'' x)) ==> ('h4/const/list/EVERY' P l1 <=> 'h4/const/list/EVERY' 'P\'' l2)
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_3f6114,V_3f6110]: ![F, G]: (![X]: s(V_3f6110,happ(s(fun(V_3f6114,V_3f6110),F),s(V_3f6114,X))) = s(V_3f6110,happ(s(fun(V_3f6114,V_3f6110),G),s(V_3f6114,X))) => s(fun(V_3f6114,V_3f6110),F) = s(fun(V_3f6114,V_3f6110),G))).
fof('h4/thm/list/EVERY_CONG_', conjecture, ![A]: ![L1, L2, P, V_27P_5c_27_27]: ((s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),L2) & ![X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L2)))))) => s(bool,happ(s(fun(A,bool),P),s(A,X))) = s(bool,happ(s(fun(A,bool),V_27P_5c_27_27),s(A,X))))) => s(bool,'h4/const/list/EVERY'(s(fun(A,bool),P),s('h4/type/list/list'(A),L1))) = s(bool,'h4/const/list/EVERY'(s(fun(A,bool),V_27P_5c_27_27),s('h4/type/list/list'(A),L2))))).
