%   ORIGINAL: 'h4/thm/list/EVERY2_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 'l1\'' l2 'l2\'' P 'P\''. l1 = 'l1\'' /\ l2 = 'l2\'' /\ (!x y. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' 'l1\'') /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' 'l2\'') ==> (P x y <=> 'P\'' x y)) ==> ('h4/const/list/LIST_REL' P l1 l2 <=> 'h4/const/list/LIST_REL' 'P\'' 'l1\'' '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 'l1\'' l2 'l2\'' P 'P\''. l1 = 'l1\'' /\ l2 = 'l2\'' /\ (!x y. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' 'l1\'') /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' 'l2\'') ==> (happ (happ P x) y <=> happ (happ 'P\'' x) y)) ==> ('h4/const/list/LIST_REL' P l1 l2 <=> 'h4/const/list/LIST_REL' 'P\'' 'l1\'' '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_3f7490,V_3f7486]: ![F, G]: (![X]: s(V_3f7486,happ(s(fun(V_3f7490,V_3f7486),F),s(V_3f7490,X))) = s(V_3f7486,happ(s(fun(V_3f7490,V_3f7486),G),s(V_3f7490,X))) => s(fun(V_3f7490,V_3f7486),F) = s(fun(V_3f7490,V_3f7486),G))).
fof('h4/thm/list/EVERY2_cong_', conjecture, ![A,B]: ![L1, V_27l1_5c_27_27, L2, V_27l2_5c_27_27, P, V_27P_5c_27_27]: ((s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),V_27l1_5c_27_27) & (s('h4/type/list/list'(B),L2) = s('h4/type/list/list'(B),V_27l2_5c_27_27) & ![X, Y]: ((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),V_27l1_5c_27_27)))))) & p(s(bool,'h4/const/bool/IN'(s(B,Y),s(fun(B,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(B),V_27l2_5c_27_27))))))) => s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,X))),s(B,Y))) = s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),V_27P_5c_27_27),s(A,X))),s(B,Y)))))) => s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),P),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2))) = s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),V_27P_5c_27_27),s('h4/type/list/list'(A),V_27l1_5c_27_27),s('h4/type/list/list'(B),V_27l2_5c_27_27))))).
