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Proof step 13 from proof keys-in-elim (previous step)

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)

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 14:
fs[adr0].key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = fs[adr0].key), 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)

Rule argument

pos: left 2 terms: fs[adr0].key, fs

Additional information

Used terms: fs[adr0].key, fs