# Right identity element

THEOREM

One is a right identity element of natural number exponentiation.

$$\forall x \in \mathbb{N} : x^1 = x$$

Proof unavailable

LEMMA

Zero is a right identity element of rational number addition.

$$\forall x \in \mathbb{Q} : x + 0 = x$$

Proof available

THEOREM

True is a right identity element of conjunction.

$$P \wedge \top \dashv\vdash \top$$

Proof available

LEMMA

One is a right identity element of natural number multiplication.

$$\forall x \in \mathbb{N} : x * 1 = x$$

Proof available

THEOREM

False is a right identity element of disjunction.

$$P \wedge \bot \dashv\vdash \bot$$

Proof available

LEMMA

Zero is a right identity element of natural number addition.

$$\forall x \in \mathbb{N} : x + 0 = x$$

Proof available

LEMMA

Zero is a right identity element of integer addition.

$$\forall x \in \mathbb{Z} : x + 0 = x$$

Proof available