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Proof step 1 from proof iterate-subseq-leq (conclusion)

monotone(f), m ≤ n ⊦ ((f ^ m))(λ x. false) ⊆ ((f ^ n))(λ x. false)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
monotone(f), 0 ≤ n ⊦ ((f ^ 0))(λ x. false) ⊆ ((f ^ n))(λ x. false)
Proof step 5:
∀ f, n. monotone(f) ∧ m0 ≤ n → ((f ^ m0))(λ x. false) ⊆ ((f ^ n))(λ x. false), monotone(f), m0 +1 ≤ n ⊦ ((f ^ m0 +1))(λ x. false) ⊆ ((f ^ n))(λ x. false)

Rule argument

indvar: m

Additional information

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