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Proof step 8 from proof keys-at (previous step)

n ≤ # ax0, ∀ n, fs. n < # ax0 → keys(fs, ax0)[n] = fs[ax0[n]].key ∨ ax0 = [] ⊦ keys(fs, ax0)[n - 1] = fs[(adr ' + ax0)[n]].key, n = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
n = m + 1, n ≤ # ax0, ∀ n, fs. n < # ax0 → keys(fs, ax0)[n] = fs[ax0[n]].key ∨ ax0 = [] ⊦ keys(fs, ax0)[m] = fs[(adr ' + ax0)[n]].key, n = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m