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Proof step 12 from proof copy-subarray2 (previous step)

n < n1 ∨ n1 + n2 ≤ n, n + m0 < # ar1, m0 + m1 ≤ # ar1, n < m1 ⊦ copy(ar0, n0, copy(ar1, m0, mkarray(m1), 0, m1), n1, n2)[n] = ar1[n + m0], m1 = 0, # ar1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 14:
n < # copy(ar1, m0, mkarray(m1), 0, m1), n < n1 ∨ n1 + n2 ≤ n, n + m0 < # ar1, m0 + m1 ≤ # ar1, n < m1 ⊦ (n < n1 ∨ n1 + n2 ≤ n ⊃ copy(ar1, m0, mkarray(m1), 0, m1)[n];ar0[n + n0 - n1]) = ar1[n + m0], m1 = 0, # ar1 = 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, n2, n1, copy(ar1, m0, mkarray(m1), 0, m1), n0, ar0] flags: rewrite, current

Additional information

Used simplifier rules: size-copy: ⊦ # copy(ar, m, ar0, m0, n) = # ar0;%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, n2, n1, copy(ar1, m0, mkarray(m1), 0, m1), n0, ar0