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Proof step 3 from proof subdef (previous step)

∀ a. a ∈ s1 → a ∈ s2 ⊦ s1 ⊆ s2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2)
Proof step 5:
∀ a. a ∈ s1 → a ∈ s2 ⊦ ∀ a. a ∈ s1 → a ∈ s2

Rule argument

spec: set-basic inst: name: Subset seq: ⊦ s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2) subst: [s2, s1] → [s2, s1] flags: rewrite

Additional information

Used terms: s2, s1