Nuprl - Pf div_4_to

(11steps) PrintForm Definitions Lemmas int 2 Sections StandardLIB Doc

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

(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:, n:{...-1}. 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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(11steps) PrintForm Definitions Lemmas int 2 Sections StandardLIB Doc