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Proof step 9 from proof sub-insert (previous step)

∀ a0. a0 ∈ s → a0 ∈ s0 ⊦ a ∈ s0, a ∈ s, s ⊆ s0, s0 ++ a ⊆ s0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2)
Proof step 11:
∀ a0. a0 ∈ s → a0 ∈ s0 ⊦ a ∈ s0, a ∈ s, ∀ a. a ∈ s → a ∈ s0, s0 ++ a ⊆ s0

Rule argument

spec: set-basic inst: name: Subset seq: ⊦ s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2) subst: [s2, s1] → [s0, s] flags: rewrite, current

Additional information

Used terms: s0, s