Integer divides


Definition 1

ProofWiki

Definition 2

dvd_def: (?b dvd ?a) = (\k. ?a = ?b * k)
THEOREM   

One divides all integers.

$$\forall a \in \mathbb{Z} : 1 \mid a$$

Proof available

THEOREM   

Negative one divides all integers.

$$\forall a \in \mathbb{Z} : -1 \mid a$$

Proof available

THEOREM    $$\forall a,b,c \in \mathbb{Z} : a \mid b \Rightarrow a \mid c \Rightarrow a \mid b + c$$

Proof available

THEOREM    $$\forall a,b,c \in \mathbb{Z} : a \mid b \Rightarrow a \mid b + c \Rightarrow a \mid c$$

Proof available

Proper supersets