%   ORIGINAL: 'h4/thm/list/CONS_11_'
% 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: !a0 a1 'a0\'' 'a1\''. 'h4/const/list/CONS' a0 a1 = 'h4/const/list/CONS' 'a0\'' 'a1\'' <=> a0 = 'a0\'' /\ a1 = 'a1\''
%   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: !a0 a1 'a0\'' 'a1\''. 'h4/const/list/CONS' a0 a1 = 'h4/const/list/CONS' 'a0\'' 'a1\'' <=> a0 = 'a0\'' /\ a1 = 'a1\''
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_3f2938,V_3f2934]: ![F, G]: (![X]: s(V_3f2934,happ(s(fun(V_3f2938,V_3f2934),F),s(V_3f2938,X))) = s(V_3f2934,happ(s(fun(V_3f2938,V_3f2934),G),s(V_3f2938,X))) => s(fun(V_3f2938,V_3f2934),F) = s(fun(V_3f2938,V_3f2934),G))).
fof('h4/thm/list/CONS_11_', conjecture, ![A]: ![A0, A1, V_27a0_5c_27_27, V_27a1_5c_27_27]: (s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,A0),s('h4/type/list/list'(A),A1))) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,V_27a0_5c_27_27),s('h4/type/list/list'(A),V_27a1_5c_27_27))) <=> (s(A,A0) = s(A,V_27a0_5c_27_27) & s('h4/type/list/list'(A),A1) = s('h4/type/list/list'(A),V_27a1_5c_27_27)))).
