%   ORIGINAL: 'h4/thm/list/EQ_LIST_'
% 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: !h1 h2. h1 = h2 ==> (!l1 l2. l1 = l2 ==> 'h4/const/list/CONS' h1 l1 = 'h4/const/list/CONS' h2 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: !h1 h2. h1 = h2 ==> (!l1 l2. l1 = l2 ==> 'h4/const/list/CONS' h1 l1 = 'h4/const/list/CONS' h2 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_3f3063,V_3f3059]: ![F, G]: (![X]: s(V_3f3059,happ(s(fun(V_3f3063,V_3f3059),F),s(V_3f3063,X))) = s(V_3f3059,happ(s(fun(V_3f3063,V_3f3059),G),s(V_3f3063,X))) => s(fun(V_3f3063,V_3f3059),F) = s(fun(V_3f3063,V_3f3059),G))).
fof('h4/thm/list/EQ_LIST_', conjecture, ![A]: ![H1, H2]: (s(A,H1) = s(A,H2) => ![L1, L2]: (s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),L2) => s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H1),s('h4/type/list/list'(A),L1))) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H2),s('h4/type/list/list'(A),L2)))))).
