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Proof step 6 from proof payload-copy-right-upper (previous step)

n + nused0 + 1 < # zbrar, n + 1 < # copy(zbrar, n, zbrar, n + 1, nused0 + 1), ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ (copy(zbrar, n, zbrar, n + 1, nused0 + 1)[n + 1].entry? ⊃ payload(copy(zbrar, n, zbrar, n + 1, nused0 + 1), (n + 1) + 1, nused0) [copy(zbrar, n, zbrar, n + 1, nused0 + 1)[n + 1].key, copy(zbrar, n, zbrar, n + 1, nused0 + 1)[n + 1].adr ] ;payload(copy(zbrar, n, zbrar, n + 1, nused0 + 1), (n + 1) + 1, nused0) ) = payload(zbrar, n, nused0 + 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
n + nused0 + 1 < # zbrar, n + 1 < # zbrar, ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ (zbrar[2 * n - n].entry? ⊃ payload(copy(zbrar, n, zbrar, n + 1, nused0 + 1), 2 + n, nused0)[zbrar[2 * n - n].key, zbrar[2 * n - n].adr] ;payload(copy(zbrar, n, zbrar, n + 1, nused0 + 1), 2 + n, nused0) ) = payload(zbrar, n, nused0 + 1)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n - n + n1 = m - n1; (s)% ⊦ m + m = 2 * m; (s)%n0 < n ⊦ ¬ m + (* n) ≤ (* n0); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)%⊦ m0 < # zbrar → copy(zbrar0, n, zbrar, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ zbrar[m0];zbrar0[m0 + n - n0]); (s)% ⊦ # copy(zbrar, m, zbrar0, m0, n) = # zbrar0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic