Library
▹
Essentials
▹
Functions
Proposition 1.5.36.
Let
X
be a set,
n
∈
ℕ
. Then:
(id
X
)
n
=
id
X
Proof.
By induction on
n
.
(id
X
)
0
=
id
X
.
Let
x
∈
ℕ
such that
(id
X
)
x
=
id
X
. Then:
(id
X
)
x
+
1
=
id
X
∘ (id
X
)
x
=
id
X
∘ id
X
=
1.5.13
id
X