Nuprl - Pf div_2_to

(10steps) PrintForm Definitions Lemmas int 2 Sections StandardLIB Doc

1. a: {...0}
2. b:

(a b) = -((-a) b)

By: Inst Thm* a:, n:. a = (a n)n+(a rem n) [-a;b] THEN Inst Thm* a:, n:. 0(a rem n) & (a rem n) < n [-a;b] THEN Inst Thm* a:, n:. a = (a n)n+(a rem n) [a;b] THEN Inst Thm* a:{...0}, n:. 0(a rem n) & (a rem n) > -n [a;b]

Generated subgoal:

1 3. -a = ((-a) b)b+((-a) rem b)
4. 0((-a) rem b) & ((-a) rem b) < b
5. a = (a b)b+(a rem b)
6. 0(a rem b) & (a rem b) > -b
(a b) = -((-a) b)

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(10steps) PrintForm Definitions Lemmas int 2 Sections StandardLIB Doc