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Proof step 8 from proof subarray-copy (previous step)

n < m1, m0 + m1 ≤ # ar1 ⊦ copy(copy(ar0, n0, ar1, n3 + m0, n2), m0, mkarray(m1), 0, m1)[n] = copy(ar0, n0, copy(ar1, m0, mkarray(m1), 0, m1), n3, n2)[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 10:
n < m1, n < # mkarray(m1), m0 + m1 ≤ # ar1 ⊦ (n < 0 ∨ 0 + m1 ≤ n ⊃ mkarray(m1)[n];copy(ar0, n0, ar1, n3 + m0, n2)[n + m0 - 0]) = copy(ar0, n0, copy(ar1, m0, mkarray(m1), 0, m1), n3, n2)[n]

Rule argument

spec: <toplevel> 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, ar1, n3 + m0, n2)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # mkarray(n) = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n, m1, 0, mkarray(m1), m0, copy(ar0, n0, ar1, n3 + m0, n2)