%   ORIGINAL: 'h4/thm/seq/SEQ_MONO_LE_'
% 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 x n. (!n0. 'h4/const/real/real_lte' (f n0) (f ('h4/const/arithmetic/+' n0 ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))))) /\ 'h4/const/seq/-->' f x ==> 'h4/const/real/real_lte' (f n) x
%   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 x n. (!n0. 'h4/const/real/real_lte' (happ f n0) (happ f ('h4/const/arithmetic/+' n0 ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))))) /\ 'h4/const/seq/-->' f x ==> 'h4/const/real/real_lte' (happ f n) x
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_3f65936,V_3f65932]: ![F, G]: (![X]: s(V_3f65932,happ(s(fun(V_3f65936,V_3f65932),F),s(V_3f65936,X))) = s(V_3f65932,happ(s(fun(V_3f65936,V_3f65932),G),s(V_3f65936,X))) => s(fun(V_3f65936,V_3f65932),F) = s(fun(V_3f65936,V_3f65932),G))).
fof('h4/thm/seq/SEQ_MONO_LE_', conjecture, ![F, X, N]: ((![N0]: p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',N0))),s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',N0),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO')))))))))))) & p(s(bool,'h4/const/seq/-->'(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/realax/real',X))))) => p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',N))),s('h4/type/realax/real',X)))))).
