%   ORIGINAL: 'h4/thm/list/LLEX_THM_e2'
% 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: !t2 t1 h2 h1 R. 'h4/const/list/LLEX' R ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2) <=> R h1 h2 \/ h1 = h2 /\ 'h4/const/list/LLEX' R t1 t2
%   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: !t2 t1 h2 h1 R. 'h4/const/list/LLEX' R ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2) <=> happ (happ R h1) h2 \/ h1 = h2 /\ 'h4/const/list/LLEX' R t1 t2
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_3f11219,V_3f11215]: ![F, G]: (![X]: s(V_3f11215,happ(s(fun(V_3f11219,V_3f11215),F),s(V_3f11219,X))) = s(V_3f11215,happ(s(fun(V_3f11219,V_3f11215),G),s(V_3f11219,X))) => s(fun(V_3f11219,V_3f11215),F) = s(fun(V_3f11219,V_3f11215),G))).
fof('h4/thm/list/LLEX_THM_e2', conjecture, ![A]: ![T2, T1, H2, H1, R]: (p(s(bool,'h4/const/list/LLEX'(s(fun(A,fun(A,bool)),R),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H1),s('h4/type/list/list'(A),T1))),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H2),s('h4/type/list/list'(A),T2)))))) <=> (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,H1))),s(A,H2)))) | (s(A,H1) = s(A,H2) & p(s(bool,'h4/const/list/LLEX'(s(fun(A,fun(A,bool)),R),s('h4/type/list/list'(A),T1),s('h4/type/list/list'(A),T2)))))))).
