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Proof step 4 from proof btree-write-node (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), height = 0, ((btree(rp, r, adr0, height, dirty, ri, iast, as, alladrs, nstat) * P))(zh), btree-sub-clean(r, m0, zh), r ∈ zh, as ⊆ alladrs, as ⊆ dom iast, height = 0 → as = ∅ ⊦ ((btree(rp, r, adr1, height, false, ri, iast[adr1, save(mkznode(r0, zbrar, boolvar, true, m0))], as ++ adr1, (alladrs -- adr0) ++ adr1, nstat) * P) )(zh[r, mkznode(r0, zbrar, boolvar, false, m0)]), adr0 ∈ as, adr1 ∈ alladrs, adr1 ∈ iast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
zh[r] = mkznode(r0, zbrar, boolvar, true, m0), ((btree(rp, r, adr0, 0, dirty, ri, iast, ∅, ∅ ++ adr0, nstat) * P))(zh), btree-sub-clean(r, m0, zh), r ∈ zh ⊦ adr1 = adr0, ((btree(rp, r, adr1, 0, false, ri, iast[adr1, save(mkznode(r0, zbrar, boolvar, true, m0))], ∅ ++ adr1, ∅ ++ adr1, nstat) * P) )(zh[r, mkznode(r0, zbrar, boolvar, false, m0)]), adr1 ∈ iast

Rule argument

Additional information

Used simplifier rules: btree-leaf-adr: ⊦ ((btree(rp, r, adr, 0, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → alladrs = {adr} ;%btree-dirty-adr-notin: ⊦ r ∈ zh ∧ zh[r] = mkznode(rp0, zbrar, boolvar, true, height0) ∧ (( btree (rp, r, adr, height, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → ¬ adr ∈ as ∧ (height = 0 → as = ∅);%btree-refed-subseteq-alladrs: ⊦ (( btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ alladrs;%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast;% ⊦ ¬ adr ∈ as → (as ++ adr = ∅ ++ adr0 ↔ adr = adr0 ∧ as = ∅); (ws)% ⊦ adr ∈ ∅ ++ adr0 ↔ adr = adr0; (s)% ⊦ ∅ -- adr = ∅; (s)% ⊦ (as ++ adr) -- adr = as -- adr; (s)% ⊦ ¬ adr ∈ ∅; (s)% ⊦ ∅ ⊆ as; (s)% ⊦ {adr} = ∅ ++ adr; (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]