Nuprl - Proof: nsub discr range surj 1 2 1 1 1 2

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At: nsub discr range surj 1 2 1 1 1 2

1. A : Type
2. A Discrete
3. k :

4. f :

k

A
5. {a:A|

i:

k. a = f(i) }

Type
6. f

k

{a:A|

i:

k. a = f(i) }
7. b : A
8.

i:

k. b = f(i) [not for witness]
9. e : A

A

10.

x,y:A. (x e y)

x = y
11. (

j.(f(j)) e b)

{p:(

k

)|

i:

k. p(i) }
12. (least i:

. (f(i)) e b)

k

a:

k. f(a) = b

{a:A|

i:

k. a = f(i)

A }

By:	Witness: least i:. (f(i)) e b

Generated subgoal:

1 8. i:k. b = f(i)
9. e : AA
10. x,y:A. (x e y)  x = y
11. (j.(f(j)) e b)  {p:(k)| i:k. p(i) }
12. (least i:. (f(i)) e b)  k
  f(least i:. (f(i)) e b) = b  {a:A| i:k. a = f(i) }
4 steps

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(16steps total) PrintForm Definitions Lemmas DiscreteMath Sections DiscrMathExt Doc