Basis step: to prove that P(a)≡TP( a ) \equiv T, where aa is the smallest element in the domain of nn.

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

Inductive step: to prove that ∀k(P(k)→P(k+1))≡T∀k(P(k)→P(k+1))≡T\forall k ( P( k ) \to P( k+1 ) ) \equiv T.

proof

QED