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Proof step 26 from proof cut (previous step)

# ar = m + 1, n ≤ m ⊦ ar[n] = copy(ar, 1, mkarray(m + 1), 1, m)[n], ar = [], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])

Rule argument

spec: array-copy 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, m, 1, mkarray(m + 1), 1, ar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ # mkarray(n) = n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s) Used terms: n, m, 1, mkarray(m + 1), 1, ar