Peano arithmetic


THEOREM    $$\forall x \in \mathbb{N} : x + \Suc(y) = \Suc(x + y)$$

Proof available

THEOREM    $$\forall x,y \in \mathbb{N} : x * \Suc(y) = x + x * y$$

Proof available

THEOREM   

Multiplication is left-distributive over addition.

$$\forall x,y,z \in \mathbb{N} : x * (y + z) = x * y + x * z$$

Proof available

THEOREM   

Multiplication is right-distributive over addition.

$$\forall x,y,z \in \mathbb{N} : (y + z) * x = y * x + z * x$$

Proof available

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