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Proof step 8 from proof put-sw-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m ≤ # x0, ∀ m, n, a. m < # x0 ∧ n < # x0 → (a ∈ x0[m, x0[n]][n, x0[m]] ↔ a ∈ x0) ⊦ m = 0, a ∈ (a0 ' + x0)[m, a0][0, x0[m - 1]] ↔ a = a0 ∨ a ∈ x0

Rule argument

Additional information

Used simplifier rules: e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list