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Proof step 13 from proof dups-firstoc-rew (previous step)

a ∈ x0 ⊦ dups(x0), ∃ y0, a1, z0. a ' + x0 = y0 + a1 ' + z0 ∧ a1 ∈ y0 ∧ ¬ dups(y0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ a ∈ x ↔ (∃ y, z. x = y + a ' + z ∧ ¬ a ∈ y)
Proof step 15:
∃ y, z. x0 = y + a ' + z ∧ ¬ a ∈ y ⊦ dups(x0), ∃ y0, a1, z0. a ' + x0 = y0 + a1 ' + z0 ∧ a1 ∈ y0 ∧ ¬ dups(y0)

Rule argument

spec: list inst: name: firstoc-rew seq: ⊦ a ∈ x ↔ (∃ y, z. x = y + a ' + z ∧ ¬ a ∈ y) subst: [x, a] → [x0, a] flags: rewrite

Additional information

Used terms: x0, a