Natural number less than


THEOREM   

Natural number less than is transitive.

Proof available

THEOREM    \(\forall a,b,c \in \mathbb{N} : a \lt b \Rightarrow c + a \lt c + b\)

Proof available

THEOREM    \(\forall a,b,c \in \mathbb{N} : a \lt b \Rightarrow a + c \lt b + c\)

Proof available

THEOREM    \(\forall a,b,c,d \in \mathbb{N} : a \lt b \wedge c \lt d \Rightarrow a + c \lt b + d\)

Proof available