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Proof step 1 from proof Subset (conclusion)

⊦ st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ lookup(a, st1) = lookup(a, st2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a])
Proof step 3:
⊦ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a]) ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ lookup(a, st1) = lookup(a, st2))

Rule argument

spec: store inst: name: Subset seq: ⊦ st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a]) subst: [st2, st1] → [st2, st1] flags: rewrite

Additional information

Used terms: st2, st1