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Proof step 9 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 = fs[adr].key, ∃ adr0. adr0 ∈ ax0 ∧ fs[adr0].key = key

Heuristic quantifier closing applied rule all left

And obtained the following new goals

Proof step 10:
key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = key), 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

Rule argument

pos: left 2 terms: key, fs

Additional information

Used terms: key, fs