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Proof step 9 from proof append-a (previous step)

n < (# ar + # ar0) + # ar1, # ar + # ar0 ≤ n ⊦ # ar1 = 0, ((ar + ar0) + ar1)[n] = (ar + ar0 + ar1)[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: append-at2 seq: ⊦ # ar0 ≤ n ∧ n < # ar0 + # ar1 → (ar0 + ar1)[n] = ar1[n - # ar0] subst: [n, ar1, ar0] → [n, ar1, ar + ar0] flags: <all paths>

Additional information

Used simplifier rules: append-len: ⊦ #(ar0 + ar1) = # ar0 + # ar1;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n, ar1, ar + ar0