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Proof step 1 from proof subset-rec (conclusion)

⊦ a ' + x ⊆ y ↔ a ∈ y ∧ x ⊆ y

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y)
Proof step 3:
⊦ (∀ a0. a0 ∈ a ' + x → a0 ∈ y) ↔ a ∈ y ∧ x ⊆ y

Rule argument

spec: list-set inst: name: subset seq: ⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y) subst: [y, x] → [y, a ' + x] flags: rewrite, current

Additional information

Used terms: y, a ' + x