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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: in-empty: ⊦ ¬ a ∈ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%mk-empty: ⊦ mklist(a, m) = [] ↔ m = 0; from specification list-last%del1-e: ⊦ [] -1l a = []; from specification list-del