%   ORIGINAL: 'h4/thm/rich_list/IS_PREFIX_APPENDS_'
% 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: !a b c. 'h4/const/list/isPREFIX' ('h4/const/list/APPEND' a b) ('h4/const/list/APPEND' a c) <=> 'h4/const/list/isPREFIX' b c
%   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: !a b c. 'h4/const/list/isPREFIX' ('h4/const/list/APPEND' a b) ('h4/const/list/APPEND' a c) <=> 'h4/const/list/isPREFIX' b c
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_3f56911,V_3f56907]: ![F, G]: (![X]: s(V_3f56907,happ(s(fun(V_3f56911,V_3f56907),F),s(V_3f56911,X))) = s(V_3f56907,happ(s(fun(V_3f56911,V_3f56907),G),s(V_3f56911,X))) => s(fun(V_3f56911,V_3f56907),F) = s(fun(V_3f56911,V_3f56907),G))).
fof('h4/thm/rich_list/IS_PREFIX_APPENDS_', conjecture, ![A]: ![A0, B, C]: s(bool,'h4/const/list/isPREFIX'(s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),A0),s('h4/type/list/list'(A),B))),s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),A0),s('h4/type/list/list'(A),C))))) = s(bool,'h4/const/list/isPREFIX'(s('h4/type/list/list'(A),B),s('h4/type/list/list'(A),C)))).
