Nuprl - Proof: iter via intseg comp binop 1 2 1 2 1 1 1 1 1

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At: iter via intseg comp binop 1 2 1 2 1 1 1 1 1

1. A : Type
2. f : A

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

b:{...a}, e,g:({a..b

}

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

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

}. g(i))
8. =
8. (Iter(f;u) i:{a..b

}. f(e(i),g(i)))
9. b : {a...}
10.

c:{a..b

}, e,g:({a..c

}

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

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

}. g(i))
10. =
10. (Iter(f;u) i:{a..c

}. f(e(i),g(i)))
11. {a..b

}

A
12. {a..b

}

A
13.

a = b
14. U : A
15. X : A
16. V : A
17. A

f(f(U,X),V) = f(f(U,V),X)

By:	Rewrite by is_assoc_sep(A; f)

Generated subgoal:

1 f(U,f(X,V)) = f(U,f(V,X))
2 steps

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