Nuprl - Proof: iter via intseg shift rw 1 2

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At: iter via intseg shift rw 1 2

1. A : Type
2. f : A

A
3. u : A
4. a :

5. b : {a+1...}
6.

c:{a..b

}, e:({a..c

}

A), k:

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

}. e(i)) = (Iter(f;u) j:{a+k..c+k

}. e(j-k))
7. e : {a..b

}

A
8. k :

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

}. e(i)) = (Iter(f;u) j:{a+k..b+k

}. e(j-k))

By:	Rewrite by Thm* f:(AAA), u:A, a,b:, e:({a..b}A). Thm* a<b Thm* Thm* (Iter(f;u) i:{a..b}. e(i)) = f((Iter(f;u) i:{a..b-1}. e(i)),e(b-1))

Generated subgoal:

1   f((Iter(f;u) i:{a..b-1}. e(i)),e(b-1))
  =
  f((Iter(f;u) j:{a+k..b+k-1}. e(j-k)),e(b+k-1-k))
3 steps

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