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Proof step 1 from proof dom-gstore-crash (conclusion)

⊦ dom crash(gstore, gstore0, ginval, nx) = dom gstore ∪ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 3:
⊦ ∀ n. n ∈ dom crash(gstore, gstore0, ginval, nx) ↔ n ∈ dom gstore ∪ ginval

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [dom gstore ∪ ginval, dom crash(gstore, gstore0, ginval, nx)] flags: <all paths>

Additional information

Used terms: dom gstore ∪ ginval, dom crash(gstore, gstore0, ginval, nx)