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Proof step 11 from proof perm-mklist (previous step)

x -1l a = mklist(a, n0), a ∈ x ⊦ x = a ' + (x -1l a), x.head = a ∧ x ≠ []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
x -1l a = mklist(a, n0), a ∈ x ⊦ x.head = a, x = a ' + mklist(a, n0), x = []

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ []; (s)% ⊦ mklist(a, m) = [] ↔ m = 0; (s)% ⊦ [] -1l a = []; (s)