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Proof step 12 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) ∧ ¬ @(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)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
gstore[m] = groupblock(gndx, lax, m2) ⊦ (@(m, m0, m1) ∈ gstore ∧ 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)])

Rule argument

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);% ⊦ adr ∈ dom fs ↔ adr ∈ fs; (s)% ⊦ @(m, m0, m1) ∈ as | m ↔ @(m, m0, m1) ∈ as; (s)% ⊦ @(m, m0, m1).lnum = m; (s)