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Proof step 3 from proof restr-add-notin (previous step)

⊦ (ns ++ n) \ dom gstore = (ns \ dom gstore) ++ n, n ∈ gstore

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 5:
⊦ n ∈ gstore, ∀ n0. n0 ∈ (ns ++ n) \ dom gstore ↔ n0 ∈ (ns \ dom gstore) ++ n

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [(ns \ dom gstore) ++ n, (ns ++ n) \ dom gstore] flags: <all paths>

Additional information

Used terms: (ns \ dom gstore) ++ n, (ns ++ n) \ dom gstore