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Proof step 5 from proof subarray-copy-elim (previous step)

n0 < n, n0 < n1, m1 + n ≤ # ar1, n1 ≤ n ⊦ n1 = 0, copy(copy(ar0, m0, ar1, m1, n), m1, mkarray(n1), 0, n1)[n0] = copy(ar0, m0, mkarray(n1), 0, n1)[n0], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 7:
n0 < # mkarray(n1), n0 < n, n0 < n1, m1 + n ≤ # ar1, n1 ≤ n ⊦ n1 = 0, (n0 < 0 ∨ 0 + n1 ≤ n0 ⊃ mkarray(n1)[n0];copy(ar0, m0, ar1, m1, n)[n0 + m1 - 0]) = copy(ar0, m0, mkarray(n1), 0, n1)[n0], n = 0

Rule argument

spec: inst: name: at-copy seq: ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]) subst: [m0, m, n0, ar1, n, ar0] → [n0, n1, 0, mkarray(n1), m1, copy(ar0, m0, ar1, m1, n)] flags: rewrite, current

Additional information

Used simplifier rules: Size-mkarray: ⊦ # mkarray(n) = n; from specification array%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: n0, n1, 0, mkarray(n1), m1, copy(ar0, m0, ar1, m1, n)