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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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