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Proof step 5 from proof adjoin (previous step)

perm(x, y), perm(y, x), a ∈ x ⊦ perm(x, y ++ a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ a ∈ x → x ++ a = a + x

Rule argument

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

Additional information

Used simplifier rules: sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);%in: ⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y);% ⊦ a ∈ x → x ++ a = x; (s) Used terms: a, y