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Proof step 22 from proof at-payload (previous step)

zbrar[m] = mkzentry(key0, adr), zbrar[m + n1 + 1] = mkzentry(key, payload(zbrar, m + 1, nused0)[key]), key = key0, m + nused0 < # zbrar, m < # zbrar, n1 < nused0, ∀ n. ¬ n1 < n ∧ zbrar[m + n].entry? → zbrar[m + n].key ≠ key ⊦ payload(zbrar, m + 1, nused0)[key0, adr][key] = payload(zbrar, m + 1, nused0)[key]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
zbrar[m + n1 + 1] = mkzentry(key0, payload(zbrar, m + 1, nused0)[key0]), zbrar[m] = mkzentry(key0, adr), n1 < nused0, m < # zbrar, m + nused0 < # zbrar, ∀ n. ¬ n1 < n ∧ zbrar[m + n].entry? → zbrar[m + n].key ≠ key0 ⊦ adr = payload(zbrar, m + 1, nused0)[key0]

Rule argument

Additional information

Used simplifier rules: ⊦ ri[key, adr][key] = adr; (s)