%   ORIGINAL: 'h4/thm/list/EVERY2_sym_'
% 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: !R2 R1. (!x y. R1 x y ==> R2 y x) ==> (!x y. 'h4/const/list/LIST_REL' R1 x y ==> 'h4/const/list/LIST_REL' R2 y x)
%   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: !R2 R1. (!x y. happ (happ R1 x) y ==> happ (happ R2 y) x) ==> (!x y. 'h4/const/list/LIST_REL' R1 x y ==> 'h4/const/list/LIST_REL' R2 y x)
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_3f11719,V_3f11715]: ![F, G]: (![X]: s(V_3f11715,happ(s(fun(V_3f11719,V_3f11715),F),s(V_3f11719,X))) = s(V_3f11715,happ(s(fun(V_3f11719,V_3f11715),G),s(V_3f11719,X))) => s(fun(V_3f11719,V_3f11715),F) = s(fun(V_3f11719,V_3f11715),G))).
fof('h4/thm/list/EVERY2_sym_', conjecture, ![B,A]: ![R2, R1]: (![X, Y]: (p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),R1),s(A,X))),s(B,Y)))) => p(s(bool,happ(s(fun(A,bool),happ(s(fun(B,fun(A,bool)),R2),s(B,Y))),s(A,X))))) => ![X, Y]: (p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R1),s('h4/type/list/list'(A),X),s('h4/type/list/list'(B),Y)))) => p(s(bool,'h4/const/list/LIST_REL'(s(fun(B,fun(A,bool)),R2),s('h4/type/list/list'(B),Y),s('h4/type/list/list'(A),X))))))).
