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Proof step 2 from proof perm-last-rec (previous step)

⊦ perm(x, [] + a ') ↔ a ∈ x ∧ perm(x -1l a, [])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
x -1l a = [], a ∈ x ⊦ x = a '

Rule argument

Additional information

Used simplifier rules: perm-one: ⊦ perm(x, a ') ↔ x = a ';%perm-e: ⊦ perm([], []);%empty: ⊦ perm(x, []) ↔ x = [];%one-01: ⊦ a ' -1l a = []; from specification list-del%in-17: ⊦ a ∈ b ' ↔ a = b; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%Nil: ⊦ [] + x = x; from specification list