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Proof step 82 from proof splice-resize-less (previous step)

n3 < m0, # ar1 < n1 + m0, # ar1 < n1 + n2, n3 < n2, n2 ≤ m0 ⊦ copy(ar0, n0, resize(ar1, n1 + m0), n1, m0)[n3 + n1] = ar0[n3 + n0]

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] → [n3 + n1, m0, n1, resize(ar1, n1 + m0), n0, ar0] flags: <all paths>

Additional information

Used simplifier rules: resize-len: ⊦ # resize(ar, n) = n;% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m + n - m = n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss) Used terms: n3 + n1, m0, n1, resize(ar1, n1 + m0), n0, ar0