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Proof step 8 from proof nodes-crash-down (previous step)

inv(gstore \ ginval) ⊦ (¬ m ∈ ginval → (@(m, m0, m1) ∈ crash(gstore, gstore0, ginval, nx) ↓ ↔ @(m, m0, m1) ∈ gstore ↓)) ∧ ( @(m, m0, m1) ∈ crash(gstore, gstore0, ginval, nx) ↓ ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[@(m, m0, m1)] = nodes(gstore ↓, ginval)[@(m, m0, m1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 10:
inv(gstore \ ginval) ⊦ ( ¬ m ∈ ginval → ( @(m, m0, m1).lnum ∈ crash(gstore, gstore0, ginval, nx) ↓ ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ crash(gstore, gstore0, ginval, nx) ↓[@(m, m0, m1).lnum].ladrlist ↔ @(m, m0, m1) ∈ gstore ↓)) ∧ ( ( @(m, m0, m1).lnum ∈ crash(gstore, gstore0, ginval, nx) ↓ ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ crash(gstore, gstore0, ginval, nx) ↓[@(m, m0, m1).lnum].ladrlist) ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[@(m, m0, m1)] = nodes(gstore ↓, ginval)[@(m, m0, m1)])

Rule argument

spec: ablock-store-inv, inst: group-store name: in seq: ⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist subst: [gstore, adr] → [crash(gstore, gstore0, ginval, nx) ↓, @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: crash(gstore, gstore0, ginval, nx) ↓, @(m, m0, m1)