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Proof step 4 from proof btree-mark-dirty (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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-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);%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 ∈ dom iast ↔ adr ∈ iast; (s)% ⊦ ∅ ++ adr ⊆ as ↔ adr ∈ as; (s)% ⊦ adr ∈ ∅ ++ adr0 ↔ adr = adr0; (s)% ⊦ ∅ ≠ as ++ adr; (s)% ⊦ #(∅ ++ adr) = 1; (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]%one-size: ⊦ as = ∅ ++ adr → # as = 1; (forward) from specification set-basic[node-store]% ⊦ as = ∅ ++ adr → as -- adr = ∅; (s)