Equal to


Acronyms and abbreviations

reflreflexive
symsymmetric
transtransitive
THEOREM   

The equal to relation is reflexive.

$$\forall x \in S : x = x$$
refl: ?t = ?t

Proof unavailable

THEOREM   

The equal to relation is symmetric.

$$\forall x,y \in S : x = y \Rightarrow y = x$$
sym: ?s = ?t \(\Longrightarrow\) ?t = ?s

Proof unavailable

THEOREM   

The equal to relation is transitive.

$$\forall x,y,z \in S : x = y \wedge y = z \Rightarrow x = z$$
trans: ?r = ?s \(\Longrightarrow\) ?s = ?t \(\Longrightarrow\) ?r = ?t

Proof unavailable

THEOREM   

The equal to relation is an equivalence relation.

Proof available