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Proof step 11 from proof put-sw-in (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
n = m0 + 1, m ≤ # x0, n ≤ # x0, ∀ m, n, a. m < # x0 ∧ n < # x0 → (a ∈ x0[m, x0[n]][n, x0[m]] ↔ a ∈ x0) ⊦ n = 0, a ∈ (a0 ' + x0)[m, x0[m0]][n, (a0 ' + x0)[m]] ↔ a = a0 ∨ a ∈ x0

Rule argument

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

Additional information

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