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Proof step 7 from proof adjoin (previous step)

perm(x, y), a ∈ y ++ a, perm(y, x) ⊦ perm(x, (y ++ a) -1l a), a ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ a ∈ x → x ++ a = a + x

Rule argument

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

Additional information

Used simplifier rules: in: ⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y);%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);%c: ⊦ a + x = a ' + x; from specification list%in-10: ⊦ ¬ a ∈ x → (a ∈ b ' + x ↔ a = b); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%del1-y: ⊦ (a ' + x) -1l a = x; from specification list-del Used terms: a, y