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Proof step 8 from proof sym (previous step)

a ∈ y, disj(a ' + x0, y), ∀ y. disj(x0, y) → disj(y, x0) ⊦ disj(y, a ' + x0), disj(x0, y)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ disj(x, y) ↔ (∀ a. ¬(a ∈ x ∧ a ∈ y))
Proof step 10:
a ∈ y, ∀ a0. ¬(a0 ∈ a ' + x0 ∧ a0 ∈ y), ∀ y. disj(x0, y) → disj(y, x0) ⊦ disj(y, a ' + x0), disj(x0, y)

Rule argument

spec: list-dup inst: name: disjoint seq: ⊦ disj(x, y) ↔ (∀ a. ¬(a ∈ x ∧ a ∈ y)) subst: [y, x] → [y, a ' + x0] flags: rewrite, current

Additional information

Used terms: y, a ' + x0