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Proof step 10 from proof subarray-split-first (previous step)

n0 + m < # ar, n ≤ m ⊦ subarray(ar, n0, m + 1)[n] = (mkarray(1)[0, ar[n0]] + subarray(ar, n0 + 1, m))[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n0 < n → subarray(ar, m, n)[n0] = ar[m + n0]
Proof step 12:
n0 + m < # ar, n < m + 1, n ≤ m ⊦ ar[n0 + n] = (mkarray(1)[0, ar[n0]] + subarray(ar, n0 + 1, m))[n]

Rule argument

spec: array-copy name: subarray-at seq: ⊦ n0 < n → subarray(ar, m, n)[n0] = ar[m + n0] subst: [n0, n, m, ar] → [n, m + 1, n0, ar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (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 Used terms: n, m + 1, n0, ar