Basic induction over natural numbers

[edit] Weak induction

The weak induction principles for predicates is supported by the static and dynamic contexts.

Introduce

P

.

Assume

P (0)

.

Assume for all $n \in \N$ ,

P (n)

implies

P (n + 1)

.

Assert for all $n \in \N$ ,

P (n)

.

The weak induction principles for sets is also supported by the static and dynamic contexts.

Introduce

S

.

Assume $0 \in S$ .

Assume for all $n \in \N$ , $n \in S$ implies $n+1 \in S$ .

Assert for all $n \in \N$ , $n \in S$ .