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Proof step 1 from proof adjoin (conclusion)

⊦ perm(x, y) → perm(x ++ a, y ++ a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ a ∈ x → x ++ a = a + x
Proof step 3:
¬ ¬ a ∈ x ⊦ perm(x, y) → perm(x ++ a, y ++ a)
Proof step 6:
¬ a ∈ x ⊦ perm(x, y) → perm(a + x, y ++ a)

Rule argument

spec: list-dup inst: name: adjoin-notin seq: ⊦ ¬ a ∈ x → x ++ a = a + x subst: [a, x] → [a, x] flags: rewrite

Additional information

Used terms: a, x