%   ORIGINAL: 'h4/thm/list/EVERY2_mono_'
% 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: !l2 l1 R2 R1. (!x y. R1 x y ==> R2 x y) ==> 'h4/const/list/LIST_REL' R1 l1 l2 ==> 'h4/const/list/LIST_REL' R2 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: !l2 l1 R2 R1. (!x y. happ (happ R1 x) y ==> happ (happ R2 x) y) ==> 'h4/const/list/LIST_REL' R1 l1 l2 ==> 'h4/const/list/LIST_REL' R2 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_3f7590,V_3f7586]: ![F, G]: (![X]: s(V_3f7586,happ(s(fun(V_3f7590,V_3f7586),F),s(V_3f7590,X))) = s(V_3f7586,happ(s(fun(V_3f7590,V_3f7586),G),s(V_3f7590,X))) => s(fun(V_3f7590,V_3f7586),F) = s(fun(V_3f7590,V_3f7586),G))).
fof('h4/thm/list/EVERY2_mono_', conjecture, ![A,B]: ![L2, L1, 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(B,bool),happ(s(fun(A,fun(B,bool)),R2),s(A,X))),s(B,Y))))) => (p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R1),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2)))) => p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R2),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2))))))).
