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Proof step 5 from proof keys-in-elim-last-oc (previous step)

key ∈ keys(fs, ax0) → (∃ ax2, ax1, adr. ax0 = ax2 + adr ' + ax1 ∧ fs[adr].key = key ∧ ¬ fs[adr].key ∈ keys(fs, ax1)), key = fs[adr].key ∨ key ∈ keys(fs, ax0) ⊦ ∃ ax, ax1, adr0. adr ' + ax0 = ax + adr0 ' + ax1 ∧ fs[adr0].key = key ∧ ¬ fs[adr0].key ∈ keys(fs, ax1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
key ∈ keys(fs, ax0) → ax0 = ax + adr0 ' + ax1 ∧ fs[adr0].key = key ∧ ¬ fs[adr0].key ∈ keys(fs, ax1), key = fs[adr].key ∨ key ∈ keys(fs, ax0) ⊦ ∃ ax, ax1, adr0. adr ' + ax0 = ax + adr0 ' + ax1 ∧ fs[adr0].key = key ∧ ¬ fs[adr0].key ∈ keys(fs, ax1)

Proof step 5 from proof keys-in-elim-last-oc (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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