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Proof step 15 from proof btree-inv-alloc (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
((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

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s)%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]%sub-in: ⊦ adr ∈ as ∧ as ⊆ as0 → adr ∈ as0; (forward) from specification set-basic[node-store]%⊦ ¬ n ∈ istore ∧ adr ∈ istore → nodes(istore[n, iblock])[adr] = istore[adr]; (s)% ⊦ ¬ n ∈ istore ∧ adr ∈ istore → adr ∈ istore[n, iblock]; (ss)% ⊦ adr ∈ nodes(istore) ↔ adr ∈ istore; (s)% ⊦ adr ∈ iast | as ↔ adr ∈ iast ∧ adr ∈ as; (ws)