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Proof step 9 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 ∈ gstore ∧ @(m0, m1) ∈ gstore[m].ladrlist ∧ m ≠ n ∧ ¬ m ∈ ginval → nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = (nodes(gstore, ginval) \ (dom nodes(gstore, ginval) | n))[@(m, m0, m1)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
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)])

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[m], gndx, lax, m2]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[m], gndx, lax, m2