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Proof step 17 from proof put-at (previous step)

m0 < # x0, ∀ m, a, n. m < # x0 → x0[m, a][n] = x0[n] ∨ m = n ⊦ m0 + 1 = n, x0[m0, a][n - 1] = (a0 ' + x0)[n], n = 0, x0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
n = m1 + 1, m0 < # x0, ∀ m, a, n. m < # x0 → x0[m, a][n] = x0[n] ∨ m = n ⊦ m0 + 1 = n, x0[m0, a][m1] = (a0 ' + x0)[n], n = 0, x0 = []

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m1