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Proof step 1 from proof insperm (conclusion)

⊦ perm(a ' + x, ins≤(a, x))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ perm(a ' + x, y) ↔ ¬ ¬(a ∈ y ∧ perm(x, y -1l a))

Rule argument

spec: list-perm inst: name: del-01 seq: ⊦ perm(a ' + x, y) ↔ ¬ ¬(a ∈ y ∧ perm(x, y -1l a)) subst: [y, x, a] → [ins≤(a, x), x, a] flags: rewrite

Additional information

Used simplifier rules: in-04: ⊦ a ∈ ins≤(a, x);%del1-02: ⊦ ins≤(a, x) -1l a = x;%ref: ⊦ perm(x, x); from specification list-perm Used terms: ins≤(a, x), x, a