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Proof step 44 from proof splice-resize-less (previous step)

n2 < m0, n < n1 + m0, n + 1 < n1 + m0, n < n2 + n1, n < # ar1, # ar1 < n1 + m0, n1 + n2 ≤ # ar1 ⊦ copy(ar0, n0, resize(ar1, n1 + m0), n1, m0)[n] = (n < n1 ⊃ ar1[n];ar0[n + n0 - n1]), n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

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, m0, n1, resize(ar1, n1 + m0), n0, ar0] flags: <all paths>

Additional information

Used simplifier rules: resize-len: ⊦ # resize(ar, n) = n;%resize-at: ⊦ m < n → resize(ar, n)[m] = (# ar ≤ m ∧ m < n ⊃ zero;ar[m]);% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss) Used terms: n, m0, n1, resize(ar1, n1 + m0), n0, ar0