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Proof step 16 from proof nodes-dealloc (previous step)

gstore[m] = groupblock(gndx, lax, m2) ⊦ (m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ m ≠ n ∧ ¬ m ∈ ginval → ¬ @(m, m0, m1) ∈ dom nodes(gstore, ginval) | n) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ 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 17:
⊦ adr ∈ as | n ↔ adr.lnum = n ∧ adr ∈ as
Proof step 18:
gstore[m] = groupblock(gndx, lax, m2) ⊦ (m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ m ≠ n ∧ ¬ m ∈ ginval → ¬(@(m, m0, m1).lnum = n ∧ @(m, m0, m1) ∈ dom nodes(gstore, ginval))) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ 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-refsize-cons, inst: index-store name: restrict-leb seq: ⊦ adr ∈ as | n ↔ adr.lnum = n ∧ adr ∈ as subst: [n, as, adr] → [n, dom nodes(gstore, ginval), @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: n, dom nodes(gstore, ginval), @(m, m0, m1)