%   ORIGINAL: 'h4/thm/rich_list/SEG_0_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: !m l x. 'h4/const/arithmetic/<=' m ('h4/const/list/LENGTH' l) ==> 'h4/const/rich_list/SEG' m 'h4/const/num/0' ('h4/const/list/SNOC' x l) = 'h4/const/rich_list/SEG' m 'h4/const/num/0' l
%   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: !m l x. 'h4/const/arithmetic/<=' m ('h4/const/list/LENGTH' l) ==> 'h4/const/rich_list/SEG' m 'h4/const/num/0' ('h4/const/list/SNOC' x l) = 'h4/const/rich_list/SEG' m 'h4/const/num/0' l
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_3f53286,V_3f53282]: ![F, G]: (![X]: s(V_3f53282,happ(s(fun(V_3f53286,V_3f53282),F),s(V_3f53286,X))) = s(V_3f53282,happ(s(fun(V_3f53286,V_3f53282),G),s(V_3f53286,X))) => s(fun(V_3f53286,V_3f53282),F) = s(fun(V_3f53286,V_3f53282),G))).
fof('h4/thm/rich_list/SEG_0_SNOC_', conjecture, ![A]: ![M, L, X]: (p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',M),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L)))))) => s('h4/type/list/list'(A),'h4/const/rich_list/SEG'(s('h4/type/num/num',M),s('h4/type/num/num','h4/const/num/0'),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),L))))) = s('h4/type/list/list'(A),'h4/const/rich_list/SEG'(s('h4/type/num/num',M),s('h4/type/num/num','h4/const/num/0'),s('h4/type/list/list'(A),L))))).
