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Proof step 8 from proof in-payload (previous step)

key ∈ payload(zbrar, m + 1, nused0) ↔ (∃ n. n < nused0 ∧ zbrar[(m + 1) + n].entry? ∧ zbrar[(m + 1) + n].key = key), zbrar[m].entry?, m < # zbrar, m + nused0 < # zbrar ⊦ key ∈ (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, nused0)) ↔ (∃ n. ¬ nused0 < n ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
key ∈ payload(zbrar, m + 1, nused0) ↔ (∃ n. n < nused0 ∧ zbrar[(m + 1) + n].entry? ∧ zbrar[(m + 1) + n].key = key), zbrar[m].entry?, m + nused0 < # zbrar, m < # zbrar ⊦ key ∈ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr] ↔ (∃ n. ¬ nused0 < n ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key)

Proof step 8 from proof in-payload (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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