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Proof step 4 from proof putset-same (previous step)

0 < # x ⊦ x[0, x[0]] = x, x = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ x[0, x.head] = x, x = []

Rule argument

Additional information

Used simplifier rules: get-zero: ⊦ x ≠ [] → x[0] = x.head;% ⊦ # x = 0 ↔ x = []; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)