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Proof step 10 from proof nodes-dealloc (previous step)

gstore[m] = groupblock(gndx, lax, m2) ⊦ (@(m, m0, m1) ∈ gstore ∧ m ≠ n ∧ ¬ m ∈ ginval ↔ @(m, m0, m1) ∈ nodes(gstore, ginval) \ (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 11:
⊦ adr ∈ fs \ as ↔ adr ∈ fs ∧ ¬ adr ∈ as
Proof step 12:
gstore[m] = groupblock(gndx, lax, m2) ⊦ (@(m, m0, m1) ∈ gstore ∧ m ≠ n ∧ ¬ m ∈ ginval ↔ @(m, m0, m1) ∈ nodes(gstore, 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)])

Rule argument

spec: store+set, inst: node-store name: Diff-ext seq: ⊦ adr ∈ fs \ as ↔ adr ∈ fs ∧ ¬ adr ∈ as subst: [as, fs, adr] → [dom nodes(gstore, ginval) | n, nodes(gstore, ginval), @(m, m0, m1)] flags: <all paths>

Additional information

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