P:Prop. 
P 
P
2. A : Type
3.
(
n:
. A ~ n)
4. k :
5. 0<k
6. f :
(k-1)
A
7. Inj(
(k-1); A; f)
8. a : A
9.
i:(k-1). f(i) 
a
10. (
j.if j=
k-1
a else f(j) fi) 
kA
(j.if j=k-1 a else f(j) fi) k inj AP:Prop. P P
(n:. A ~ n)
(k-1)A
(k-1); A; f)
i:(k-1). f(i) a
j.if j=k-1 a else f(j) fi) kA
(j.if j=k-1 a else f(j) fi) k inj A| By: |
|
| 1 |
Inj(k; A; j.if j=k-1 a else f(j) fi) | 5 steps |
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