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Proof step 20 from proof btree-write-node (previous step)

((r => mkznode(r0, zbrar, false, true, m0) * bnode(r, zbrar, 0, m0, m0, height0 + 1, true, ri, iast, as, alladrs -- adr0) * P))(zh), btree-sub-clean(r, m0, zh), nsize(m0, nstat), adr0 ∈ alladrs, as ⊆ dom iast, as ⊆ alladrs ⊦ # alladrs = 0, alladrs = ∅, adr1 ∈ iast, adr1 ∈ alladrs, adr0 ∈ as, nsize(m0, nstat) ∧ unmodified(adr1, mkznode(r0, zbrar, false, false, m0), iast[adr1, save(mkznode(r0, zbrar, false, true, m0))]) ∧ (( r => mkznode(r0, zbrar, false, false, m0) * bnode(r, zbrar, 0, m0, m0, height0 + 1, false, ri, iast[adr1, save(mkznode(r0, zbrar, false, true, m0))], as -- adr1, alladrs -- adr0 -- adr1) * P) )(zh[r, mkznode(r0, zbrar, false, false, m0)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
((r => mkznode(r0, zbrar, false, true, m0) * bnode(r, zbrar, 0, m0, m0, height0 + 1, true, ri, iast, as, alladrs -- adr0) * P))(zh), btree-sub-clean(r, m0, zh), nsize(m0, nstat), adr0 ∈ alladrs, as ⊆ alladrs, as ⊆ dom iast ⊦ # alladrs = 0, alladrs = ∅, (( r =>_ * bnode(r, zbrar, 0, m0, m0, height0 + 1, false, ri, iast[adr1, save(mkznode(r0, zbrar, false, true, m0))], as -- adr1, alladrs -- adr0 -- adr1) * P) )(zh), adr0 ∈ as, adr1 ∈ alladrs, adr1 ∈ iast

Rule argument

Additional information

Used simplifier rules: r ∈ zh ⊦ ((r => znd * P0))(zh[r, znd0]) ↔ znd = znd0 ∧ ((r =>_ * P0))(zh); (ss)% ⊦ ((r => znd * P0))(zh) → r ∈ zh; (s)%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%⊦ unmodified (adr, mkznode(r0, zbrar, boolvar, false, m0), iast[adr, save(mkznode(r0, zbrar, boolvar, true, m0))]); (s)