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Proof step 19 from proof payload-copy-right-upper (previous step)

zbrar[n0] = mkzentry(key, adr), n0 + nused0 + 1 < # zbrar, n0 + 1 < # zbrar, n0 < # zbrar, (n0 + 1) + nused0 < # zbrar → payload(copy(zbrar, n0 + 1, zbrar, (n0 + 1) + 1, nused0), (n0 + 1) + 1, nused0) = payload(zbrar, n0 + 1, nused0), ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ payload(copy(zbrar, n0 + 1, zbrar, 2 + n0, nused0)[n0 + 1, mkzentry(key, adr)], 2 + n0, nused0)[key, adr] = payload(zbrar, n0 + 1, nused0)[key, adr]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
zbrar[n0] = mkzentry(key, adr), payload(copy(zbrar, n0 + 1, zbrar, 2 + n0, nused0), 2 + n0, nused0) = payload(zbrar, n0 + 1, nused0), n0 < # zbrar, n0 + 1 < # zbrar, n0 + nused0 + 1 < # zbrar, ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ payload(copy(zbrar, n0 + 1, zbrar, 2 + n0, nused0)[n0 + 1, mkzentry(key, adr)], 2 + n0, nused0)[key, adr] = payload(zbrar, n0 + 1, nused0)[key, adr]

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic