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Proof step 8 from proof nodes-ginval-rem-01 (previous step)

dom gstore1 ∪ ns = dom gstore ⊦ (@(m, m0, m1) ∈ gstore → (¬ m ∈ ginval \ dom gstore1 \ dom gstore ↔ ¬ m ∈ ginval)) ∧ ( @(m, m0, m1) ∈ gstore ∧ ¬ m ∈ ginval \ dom gstore1 \ dom gstore → nodes(gstore, ginval \ dom gstore1 \ dom gstore)[@(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:
dom gstore1 ∪ ns = dom gstore ⊦ ( @(m, m0, m1).lnum ∈ gstore ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ gstore[@(m, m0, m1).lnum].ladrlist → (¬ m ∈ ginval \ dom gstore1 \ dom gstore ↔ ¬ m ∈ ginval)) ∧ ( (@(m, m0, m1).lnum ∈ gstore ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ gstore[@(m, m0, m1).lnum].ladrlist) ∧ ¬ m ∈ ginval \ dom gstore1 \ dom gstore → nodes(gstore, ginval \ dom gstore1 \ dom gstore)[@(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] → [gstore, @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: gstore, @(m, m0, m1)