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Proof step 8 from proof in-keys-elim (previous step)

key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = key), ∀ key, fs. key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = key), ∃ adr0. (adr0 = adr ∨ adr0 ∈ ax0) ∧ fs[adr0].key = key ⊦ key = fs[adr].key, key ∈ keys(fs, ax0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
adr0 ∈ ax0, ∀ key, fs. key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = key) ⊦ fs[adr0].key = fs[adr].key, fs[adr0].key ∈ keys(fs, ax0), ∃ adr. adr ∈ ax0 ∧ fs[adr].key = fs[adr0].key

Proof step 8 from proof in-keys-elim (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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