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Proof step 3 from proof dom-disj-in-r (previous step)

dom gstore ∩ dom istore = ∅, n ∈ istore, 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, n ∈ istore, ∀ n. n ∈ dom gstore ∩ dom istore ↔ n ∈ ∅ ⊦

Rule argument

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

Additional information

Used terms: ∅, dom gstore ∩ dom istore