# Unique

THEOREM

Each element of a monoid has exactly one inverse element.

Proof available

THEOREM

A lattice has one top at most.

Proof available

THEOREM

A lattice has one bottom at most.

Proof available

THEOREM

The identity of a group is unique.

Proof available

THEOREM

A non-empty subset of an ordered set has one supremum at most.

Proof available

THEOREM

A non-empty subset of an ordered set has one infimum at most.

Proof available

THEOREM

An ordered set has one greatest element at most.

Proof available

THEOREM

An ordered set has one smallest element at most.

Proof available

THEOREM

The inverse of a matrix is unique.

 Premise 1 $$AB = I = BA$$ Premise 2 $$AC = I = CA$$ Conclusion $$B = C$$

Proof available

THEOREM

The empty set is unique.

Proof available

THEOREM

The identity morphism is unique.

Proof available

THEOREM

An algebraic structure has one zero element at most.

Proof available

THEOREM

An algebraic structure has one identity element at most.

Proof available