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Proof step 2 from proof btree-mark-dirty (previous step)

zh[r] = mkznode(rp0, zbrar, boolvar, false, height0), ((btree(rp, r, adr, height, false, ri, iast, as, alladrs, nstat) * P))(zh), r ∈ zh ⊦ ((btree(rp, r, adr, height, true, ri, iast, as -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
zh[r] = mkznode(rp0, zbrar, boolvar, false, height0), ((btree(rp, r, adr, height, false, ri, iast, alladrs, alladrs, nstat) * P))(zh), r ∈ zh, adr ∈ alladrs, adr ∈ iast, alladrs ⊆ dom iast, height = 0 → alladrs = ∅ ++ adr ⊦ # alladrs = 0, alladrs = ∅, ((btree(rp, r, adr, height, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)])

Rule argument

Additional information

Used simplifier rules: btree-clean-alladrs: ⊦ (( btree(rp, r, adr, height, false, ri, iast, as, alladrs, nstat) * P) )(zh) → as = alladrs;%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;%btree-clean-adr-in: ⊦ r ∈ zh ∧ zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ (( btree (rp, r, adr, height, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → adr ∈ as ∧ (height = 0 → as = ∅ ++ adr);%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]% ⊦ as ⊆ as; (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]