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Proof step 6 from proof dom-gstore-intersect-in-gstore (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: n abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ n ∈ gstore → (n ∈ dom gstore ∩ ns ↔ n ∈ ns); (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set] Used terms: n