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Proof step 13 from proof shift-03 (previous step)

perm(x1 + a0 ' + x0, y -1l a0), a0 ∈ y, perm(y -1l a0, x1 + a0 ' + x0) ⊦ a0 ∈ y -1l a0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: in seq: ⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y) subst: [a, y, x] → [a0, x1 + a0 ' + x0, y -1l a0] flags: rewrite, current

Additional information

Used simplifier rules: in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a0, x1 + a0 ' + x0, y -1l a0