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Proof step 3 from proof perm-last-rec (previous step)

x -1l a = [], a ∈ x ⊦ x = a '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ x ≠ [] → (x -1l a = [] ↔ x = a ')

Rule argument

spec: list-del name: del1-empty seq: ⊦ x ≠ [] → (x -1l a = [] ↔ x = a ') subst: [a, x] → [a, x] flags: <all paths>

Additional information

Used simplifier rules: ⊦ [] -1l a = []; (s)% ⊦ a ' ≠ []; (s)% ⊦ ¬ a ∈ []; (s) Used terms: a, x