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Proof step 6 from proof subarray-up-same (previous step)

n0 < # ar, n0 < n, n < # ar, n0 + 1 < # ar ⊦ copy(ar[n, a], 0, mkarray(n), 0, n)[n0] = copy(ar, 0, mkarray(n), 0, n)[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])

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] → [n0, n, 0, mkarray(n), 0, ar[n, a]] flags: <all paths>

Additional information

Used simplifier rules: copy-exact: # ar0 = m, # ar1 = m ⊦ copy(ar0, 0, ar1, 0, m) = ar0;%at-copy: ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]);% ⊦ ¬ m < 0; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m - 0 = m; (s)% ⊦ n < m → ar[m, a][n] = ar[n]; (s)% ⊦ # ar[n, a] = # ar; (s)% ⊦ # mkarray(n) = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss) Used terms: n0, n, 0, mkarray(n), 0, ar[n, a]