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Proof step 7 from proof selsub-diff (previous step)

∀ a. a ∈ s1 → a ∈ s2 ⊦ a ∈ s1 ↔ a ∈ s2, a1 ∈ s1 ↔ a1 ∈ s2 \ s2 \ s1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ a ∈ s1 \ s2 ↔ a ∈ s1 ∧ ¬ a ∈ s2
Proof step 9:
∀ a. a ∈ s1 → a ∈ s2 ⊦ a ∈ s1 ↔ a ∈ s2, a1 ∈ s1 ↔ a1 ∈ s2 ∧ ¬ a1 ∈ s2 \ s1

Rule argument

spec: inst: name: Difference seq: ⊦ a ∈ s1 \ s2 ↔ a ∈ s1 ∧ ¬ a ∈ s2 subst: [s2, s1, a] → [s2 \ s1, s2, a1] flags: rewrite, current

Additional information

Used terms: s2 \ s1, s2, a1