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Proof step 6 from proof nodes-dealloc (previous step)

⊦ (@(m, m0, m1) ∈ gstore ∧ m ≠ n ∧ ¬ m ∈ ginval ↔ @(m, m0, m1) ∈ nodes(gstore, ginval) \ (dom nodes(gstore, ginval) | n)) ∧ ( @(m, m0, m1) ∈ gstore -- n ∧ m ≠ n ∧ ¬ m ∈ ginval → nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = (nodes(gstore, ginval) \ (dom nodes(gstore, ginval) | n))[@(m, m0, m1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 8:
⊦ (@(m, m0, m1) ∈ gstore ∧ m ≠ n ∧ ¬ m ∈ ginval ↔ @(m, m0, m1) ∈ nodes(gstore, ginval) \ (dom nodes(gstore, ginval) | n)) ∧ ( (@(m, m0, m1).lnum ∈ gstore -- n ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ (gstore -- n)[@(m, m0, m1).lnum].ladrlist) ∧ m ≠ n ∧ ¬ m ∈ ginval → nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = (nodes(gstore, ginval) \ (dom nodes(gstore, ginval) | n))[@(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 -- n, @(m, m0, m1)] flags: <all paths>

Additional information

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