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Proof step 3 from proof crash-gstore-inv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ inv(gstore) ↔ (∀ n. n ∈ gstore → inv(gstore[n]))
Proof step 5:
dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval), inv(gstore0) ⊦ ∀ n. n ∈ crash(gstore, gstore0, ginval, nx) \ ginval → inv((crash(gstore, gstore0, ginval, nx) \ ginval)[n])

Rule argument

spec: ablock-store-inv, inst: group-store name: inv-store seq: ⊦ inv(gstore) ↔ (∀ n. n ∈ gstore → inv(gstore[n])) subst: [gstore] → [crash(gstore, gstore0, ginval, nx) \ ginval] flags: <all paths>

Additional information

Used terms: crash(gstore, gstore0, ginval, nx) \ ginval