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Proof step 6 from proof put-app-left (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
n = m + 1, n ≤ # x0, ∀ n, y, a. n < # x0 → (x0 + y)[n, a] = x0[n, a] + y ⊦ n = 0, a0 ' + (x0 + y)[m, a] = (a0 ' + x0)[n, a] + y

Rule argument

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

Additional information

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