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Proof step 11 from proof btree-restrict-union-proper (previous step)

((btree(rp, r, adr, height, dirty, ri, iast, asar[n], alladrs, nstat) * P))(zh), n < # asar, adr0 ∈ alladrs, adr0 ∈ iast, adr0 ∈ asar[n], asar[n] ⊆ dom iast, asar[n] ⊆ alladrs ⊦ # asar[n] = 0, # alladrs = 0, iast[adr0] = (iast | union(asar, 0, # asar))[adr0], asar[n] = ∅, alladrs = ∅, ((btree(rp, r, adr, height, dirty, ri, iast | union(asar, 0, # asar), asar[n], alladrs, nstat) * P))(zh)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: index-store-address-store name: restrict-at seq: ⊦ adr ∈ iast ∧ adr ∈ as → (iast | as)[adr] = iast[adr] subst: [adr, as, iast] → [adr0, union(asar, 0, # asar), iast] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ asar[n] ∧ n < m → adr ∈ union(asar, 0, m); (s) Used terms: adr0, union(asar, 0, # asar), iast