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

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