%   ORIGINAL: 'h4/thm/seq/SEQ_SUBLE_'
% 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: !f. 'h4/const/seq/subseq' f ==> (!n. 'h4/const/arithmetic/<=' n (f n))
%   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: !f. 'h4/const/seq/subseq' f ==> (!n. 'h4/const/arithmetic/<=' n (happ f n))
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_3f64886,V_3f64882]: ![F, G]: (![X]: s(V_3f64882,happ(s(fun(V_3f64886,V_3f64882),F),s(V_3f64886,X))) = s(V_3f64882,happ(s(fun(V_3f64886,V_3f64882),G),s(V_3f64886,X))) => s(fun(V_3f64886,V_3f64882),F) = s(fun(V_3f64886,V_3f64882),G))).
fof('h4/thm/seq/SEQ_SUBLE_', conjecture, ![F]: (p(s(bool,'h4/const/seq/subseq'(s(fun('h4/type/num/num','h4/type/num/num'),F)))) => ![N]: p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',N),s('h4/type/num/num',happ(s(fun('h4/type/num/num','h4/type/num/num'),F),s('h4/type/num/num',N)))))))).
