Nuprl - Proof: iter via intseg split mid 1 1 1

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At: iter via intseg split mid 1 1 1

1. A : Type
2. f : A

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

7. c :

8. a = c
9. b :

10. e : {a..b

}

A
11. a

c
12. c

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

}. e(i))

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

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

}. e(i))

By:	Rewrite by Thm* f:(AAA), u:A, a,b:, e:({a..b}A). Thm* ba (Iter(f;u) i:{a..b}. e(i)) = u Using:[a:= c \| b:= c]

Generated subgoal:

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

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