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Proof step 3 from proof keys-in-elim (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 4:
key = fs[adr].key, ∀ key, fs. key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = key) ⊦ key = fs[adr].key ∨ key ∈ keys(fs, ax0) ↔ (∃ adr0. (adr0 = adr ∨ adr0 ∈ ax0) ∧ fs[adr0].key = key)
Proof step 6:
∀ key, fs. key ∈ keys(fs, ax0) ↔ (∃ adr. adr ∈ ax0 ∧ fs[adr].key = key) ⊦ key = fs[adr].key ∨ key ∈ keys(fs, ax0) ↔ (∃ adr0. (adr0 = adr ∨ adr0 ∈ ax0) ∧ fs[adr0].key = key), key = fs[adr].key

Rule argument

fma: key = fs[adr].key

Additional information

Used formulas: key = fs[adr].key