%   ORIGINAL: 'h4/thm/integral/DIVISION_LE_SUC_'
% 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: !d a b. 'h4/const/transc/division' ('h4/const/pair/,' a b) d ==> (!n. 'h4/const/real/real_lte' (d n) (d ('h4/const/num/SUC' 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: !d a b. 'h4/const/transc/division' ('h4/const/pair/,' a b) d ==> (!n. 'h4/const/real/real_lte' (happ d n) (happ d ('h4/const/num/SUC' 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_3f40131,V_3f40127]: ![F, G]: (![X]: s(V_3f40127,happ(s(fun(V_3f40131,V_3f40127),F),s(V_3f40131,X))) = s(V_3f40127,happ(s(fun(V_3f40131,V_3f40127),G),s(V_3f40131,X))) => s(fun(V_3f40131,V_3f40127),F) = s(fun(V_3f40131,V_3f40127),G))).
fof('h4/thm/integral/DIVISION_LE_SUC_', conjecture, ![D, A, B]: (p(s(bool,'h4/const/transc/division'(s('h4/type/pair/prod'('h4/type/realax/real','h4/type/realax/real'),'h4/const/pair/,'(s('h4/type/realax/real',A),s('h4/type/realax/real',B))),s(fun('h4/type/num/num','h4/type/realax/real'),D)))) => ![N]: p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),D),s('h4/type/num/num',N))),s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),D),s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N)))))))))).
