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Proof step 3 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 4:
⊦ x = [], x[0, x.first] = x

Rule argument

Additional information

Used simplifier rules: get-zero: ⊦ x ≠ [] → x[0] = x.first;%l: ⊦ # x = 0 ↔ x = []; from specification list-data%zero: ⊦ 0 < m ↔ m ≠ 0; from specification nat-basic1