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Proof step 12 from proof subarray-split-at (previous step)

# ar = n0 + n, n1 < n0 + n ⊦ ar[n1] = (subarray(ar, 0, n) + subarray(ar, n, n0))[n1], n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: append-at1 seq: ⊦ n < # ar0 → (ar0 + ar1)[n] = ar0[n] subst: [n, ar1, ar0] → [n1, subarray(ar, n, n0), subarray(ar, 0, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(ar, m, n) = n; (s)% ⊦ n0 < n → subarray(ar, m, n)[n0] = ar[m + n0]; (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 Used terms: n1, subarray(ar, n, n0), subarray(ar, 0, n)