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Proof step 1 from proof iterate-subseq (conclusion)

monotone(f) ⊦ ((f ^ n))(λ x. false) ⊆ ((f ^ (n + 1)))(λ x. false)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
monotone(f) ⊦ ((f ^ 0))(λ x. false) ⊆ ((f ^ (0 + 1)))(λ x. false)
Proof step 7:
∀ f. monotone(f) → ((f ^ n0))(λ x. false) ⊆ ((f ^ (n0 + 1)))(λ x. false), monotone(f) ⊦ ((f ^ n0 +1))(λ x. false) ⊆ ((f ^ (n0 +1 + 1)))(λ x. false)

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;