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Proof step 17 from proof at-payload (previous step)

zbrar[m + n1 + 1] = mkzentry(key, payload(zbrar, m + 1, nused0)[key]), n1 < nused0, m < # zbrar, m + nused0 < # zbrar, ∀ n. ¬ n1 < n ∧ zbrar[m + n].entry? → zbrar[m + n].key ≠ key ⊦ (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, nused0))[key] = payload(zbrar, m + 1, nused0)[key]

User applied rule case distinction

And obtained the following new goals

Proof step 18:
zbrar[m + n1 + 1] = mkzentry(key, payload(zbrar, m + 1, nused0)[key]), zbrar[m].entry?, m + nused0 < # zbrar, m < # zbrar, n1 < nused0, ∀ n. ¬ n1 < n ∧ zbrar[m + n].entry? → zbrar[m + n].key ≠ key ⊦ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr][key] = payload(zbrar, m + 1, nused0)[key]

Rule argument

pos: right 1

Proof step 17 from proof at-payload (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information