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Proof step 6 from proof put-in-02 (previous step)

m ≤ # x0, ∀ m, a. m < # x0 → a ∈ x0[m, a] ⊦ a0 ' + x0 = [], m = 0, a ∈ (a0 ' + x0).head ' + (a0 ' + x0).tail[m -1, a]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m ≤ # x0, ∀ m, a. m < # x0 → a ∈ x0[m, a] ⊦ a = a0, m = 0, a ∈ x0[m - 1, a]

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' + x ↔ ¬(a ≠ b ∧ ¬ a ∈ x); (ss)% ⊦ n -1 = n - 1; (s)% ⊦ (a ' + x).tail = x; (s)% ⊦ (a ' + x).head = a; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)