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Proof step 8 from proof disj-union-rem (previous step)

n1 < # asar, n0 < # asar, n1 < m, n0 < m, disj(asar, 0, m), adr ∈ asar[n0] ∪ (as \ asar[n1]), m ≤ # asar ⊦ #(asar[n0] ∪ (as \ asar[n1])) = 0, n0 = n1, asar[n0] ∪ (as \ asar[n1]) = ∅, adr ∈ (asar[n0] ∪ as) \ asar[n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ as ∪ as0 ↔ adr ∈ as ∨ adr ∈ as0
Proof step 10:
n0 < m, n1 < m, n0 < # asar, n1 < # asar, disj(asar, 0, m), m ≤ # asar, adr ∈ asar[n0] ∨ adr ∈ as \ asar[n1] ⊦ #(asar[n0] ∪ (as \ asar[n1])) = 0, n0 = n1, asar[n0] ∪ (as \ asar[n1]) = ∅, adr ∈ (asar[n0] ∪ as) \ asar[n1]

Rule argument

spec: set-union, inst: address-list-set name: Union seq: ⊦ adr ∈ as ∪ as0 ↔ adr ∈ as ∨ adr ∈ as0 subst: [as0, as, adr] → [as \ asar[n1], asar[n0], adr] flags: <all paths>

Additional information

Used terms: as \ asar[n1], asar[n0], adr