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Proof step 3 from proof Subset (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ∈ st1, ∀ a. a ∈ st1 → a ∈ st2 ∧ lookup(a, st1) = lookup(a, st2) ⊦ a ∈ st2 ∧ lookup(a, st1) = lookup(a, st2)

Rule argument

Additional information

Used simplifier rules: lookup-def: ⊦ st[a] = lookup(a, st); from specification lookup