Nuprl - Proof: iter via intseg split mid 1 2

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At: iter via intseg split mid 1 2

1. A : Type
2. f : A

A

A
3. u : A
4. is_ident(A; f; u)
5. is_assoc_sep(A; f)
6. a :

7. c :

8.

a = c

b:

, e:({a..b

}

A).

a

c

c

b

(Iter(f;u) i:{a..b

}. e(i))

=

f((Iter(f;u) i:{a..c

}. e(i)),Iter(f;u) i:{c..b

}. e(i))

By:	a<c (k:, b:. (b-c = k ( ((e:({a..b}A). (((Iter(f;u) i:{a..b}. e(i)) ((= ((f((Iter(f;u) i:{a..c}. e(i)),Iter(f;u) i:{c..b}. e(i)))) Asserted

Generated subgoals:

1   a<c

  (k:, b:.
  (b-c = k
  (
  ((e:({a..b}A).
  (((Iter(f;u) i:{a..b}. e(i))
  ((=
  ((f((Iter(f;u) i:{a..c}. e(i)),Iter(f;u) i:{c..b}. e(i))))
9 steps

2 9. a<c
9.
9. (k:, b:.
9. (b-c = k
9. (
9. ((e:({a..b}A).
9. (((Iter(f;u) i:{a..b}. e(i))
9. ((=
9. ((f((Iter(f;u) i:{a..c}. e(i)),Iter(f;u) i:{c..b}. e(i))))
  b:, e:({a..b}A).
  ac

  cb

  (Iter(f;u) i:{a..b}. e(i))
  =
  f((Iter(f;u) i:{a..c}. e(i)),Iter(f;u) i:{c..b}. e(i))
2 steps

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(17steps total) Remark PrintForm Definitions Lemmas IteratedBinops Sections DiscrMathExt Doc