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Proof step 16 from proof btree-inv-alloc (previous step)

((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh0), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), inv(istore), refsize-cons(istore[n, indexblock(indx, lax, 0)], as), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), adr ∈ istore, adr0 ∈ istore, adr0 ∈ as, adr0 ∈ alladrs, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0) ⊦ # as = 0, # alladrs = 0, (nodes(istore) | as)[adr0] = istore[adr0], alladrs = ∅, as = ∅, ((btree(null, rp, adr, height, dirty, ri, nodes(istore[n, indexblock(indx, lax, 0)]), as, alladrs, ok) * true))(zh0), n ∈ istore

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, as, nodes(istore)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ istore → nodes(istore)[adr] = istore[adr]; (s)% ⊦ adr ∈ nodes(istore) ↔ adr ∈ istore; (s) Used terms: adr0, as, nodes(istore)