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Proof step 2 from proof subset-del (previous step)

x ⊆ y ⊦ ¬ x ⊆ y -l a ↔ a ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y)
Proof step 4:
x ⊆ y ⊦ ¬(∀ a0. a0 ∈ x → a0 ∈ y -l a) ↔ a ∈ x

Rule argument

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

Additional information

Used terms: y -l a, x