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Proof step 8 from proof prefixn-toset-subseteq (previous step)

∀ adr. adr ∈ ax → adr ∈ as ⊦ prefixn(n, ax).toSet ⊆ ax.toSet, ∀ adr. adr ∈ prefixn(n, ax).toSet → adr ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
adr ∈ prefixn(n, ax), ∀ adr. adr ∈ ax → adr ∈ as ⊦ adr ∈ as, prefixn(n, ax).toSet ⊆ ax.toSet

Rule argument

Additional information

Used simplifier rules: ⊦ adr ∈ ax.toSet ↔ adr ∈ ax; (s)