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Proof step 5 from proof dom-gstore-intersect-in-gstore (previous step)

n ∈ gstore, n ∈ ns, ∀ n. n ∈ ns ∩ dom gstore ↔ n ∈ ∅ ⊦ # ns = 0, ns = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n ∈ ns, n ∈ gstore, ∀ n0. ¬ n0 ∈ ns ∩ dom gstore ⊦ # ns = 0, ns = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n ∈ ∅; (s)