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Proof step 6 from proof dom-isemp (previous step)

∀ a. ¬ a ∈ st ⊦ ∀ a. (a ∈ st ↔ a ∈ ∅) ∧ st[a] = (∅)[a]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
a ∈ st, ∀ a. ¬ a ∈ st ⊦

Rule argument

Additional information

Used simplifier rules: notmemlookup: ⊦ ¬ a ∈ st → st[a] = (∅)[a]; from specification store%In-empty: ⊦ ¬ a ∈ ∅; from specification store