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Proof step 3 from proof ext-setequal (previous step)

⊦ x ⊆ y ∧ y ⊆ x ↔ (∀ a. a ∈ x ↔ a ∈ y)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y)
Proof step 5:
⊦ (∀ a. a ∈ x → a ∈ y) ∧ y ⊆ x ↔ (∀ a. a ∈ x ↔ a ∈ y)

Rule argument

spec: list-set name: subset seq: ⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y) subst: [y, x] → [y, x] flags: <all paths>

Additional information

Used terms: y, x