Inductive step: to prove that ∀k((P(a)∧⋯∧P(k))→P(k+1))≡T\forall k ( (P(a) \wedge \cdots \wedge P( k )) \to P( k+1 ) ) \equiv T, where k≥bk \geq b.

Basis step: to prove that (P(a)∧⋯∧P(b))≡T(P( a ) \wedge \cdots \wedge P(b)) \equiv T, where aa is the smallest element in the domain of nn and b≥ab\geq a is an element in the domain of nn.

Define predicate P(n)P( n ) with the domain of nn and the smallest element aa in the domain.

proof

QED