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Proof step 3 from proof subperm (previous step)

perm(x, x0), perm(x0, x), x ⊆ y ⊦ x0 ⊆ y

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

spec: list-set name: subset seq: ⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y) subst: [y, x] → [y, x0] flags: <all paths>

Additional information

Used simplifier rules: in: ⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y);%sub-notin: ⊦ x ⊆ y ∧ ¬ a ∈ y → ¬ a ∈ x; (forward) from specification list-set Used terms: y, x0