%   ORIGINAL: 'h4/thm/rich_list/IS_PREFIX_SNOC_'
% 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: !x y z. 'h4/const/list/isPREFIX' z ('h4/const/list/SNOC' x y) <=> 'h4/const/list/isPREFIX' z y \/ z = 'h4/const/list/SNOC' x y
%   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: !x y z. 'h4/const/list/isPREFIX' z ('h4/const/list/SNOC' x y) <=> 'h4/const/list/isPREFIX' z y \/ z = 'h4/const/list/SNOC' x y
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_3f56836,V_3f56832]: ![F, G]: (![X]: s(V_3f56832,happ(s(fun(V_3f56836,V_3f56832),F),s(V_3f56836,X))) = s(V_3f56832,happ(s(fun(V_3f56836,V_3f56832),G),s(V_3f56836,X))) => s(fun(V_3f56836,V_3f56832),F) = s(fun(V_3f56836,V_3f56832),G))).
fof('h4/thm/rich_list/IS_PREFIX_SNOC_', conjecture, ![A]: ![X, Y, Z]: (p(s(bool,'h4/const/list/isPREFIX'(s('h4/type/list/list'(A),Z),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),Y)))))) <=> (p(s(bool,'h4/const/list/isPREFIX'(s('h4/type/list/list'(A),Z),s('h4/type/list/list'(A),Y)))) | s('h4/type/list/list'(A),Z) = s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),Y)))))).
