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Proof step 11 from proof subarray-copy (previous step)

n < m1, m0 + m1 ≤ # ar1 ⊦ copy(ar0, n0, ar1, n3 + m0, n2)[n + m0] = 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 12:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 13:
n < m1, n < # copy(ar1, m0, mkarray(m1), 0, m1), m0 + m1 ≤ # ar1 ⊦ copy(ar0, n0, ar1, n3 + m0, n2)[n + m0] = (n < n3 ∨ n3 + n2 ≤ n ⊃ copy(ar1, m0, mkarray(m1), 0, m1)[n];ar0[n + n0 - n3])

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, n2, n3, copy(ar1, m0, mkarray(m1), 0, m1), n0, ar0] flags: <all paths>

Additional information

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