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Proof step 9 from proof iterate-subseq (previous step)

∀ f. monotone(f) → ((f ^ n0))(λ x. false) ⊆ ((f ^ (n0 + 1)))(λ x. false), monotone(f) ⊦ ((f ^ n0 +1))(λ x. false) ⊆ f(((f ^ n0 +1))(λ x. false))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
monotone(f), ∀ f. monotone(f) → ((f ^ n0))(λ x. false) ⊆ ((f ^ (n0 + 1)))(λ x. false) ⊦ ((f ^ (n0 + 1)))(λ x. false) ⊆ f(((f ^ (n0 + 1)))(λ x. false))

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2