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Proof step 2 from proof adjoin (previous step)

perm(x, y) ⊦ perm(x ++ a, y ++ a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ a ∈ x → x ++ a = a + x
Proof step 4:
perm(x, y), a ∈ x ⊦ perm(x ++ a, y ++ a)
Proof step 7:
perm(x, y) ⊦ perm(a + x, y ++ a), a ∈ x

Rule argument

spec: list-dup name: adjoin-notin seq: ⊦ ¬ a ∈ x → x ++ a = a + x subst: [a, x] → [a, x] flags: <all paths>

Additional information

Used terms: a, x