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Proof step 11 from proof btree-istore-reduce-refed (previous step)

# zbrar = BRANCH_SIZE, as -- adr = ∅, adr ∈ as ↔ ¬ dirty0, ((r => mkznode(rp, zbrar, true, dirty0, nused) * P))(zh0), nsize(nused, nstat), sorted(zbrar, 0, nused), unmodified(adr, mkznode(rp, zbrar, true, dirty0, nused), iast0), nused ≤ BRANCH_SIZE, iast0 | as ⊆ iast1, as ⊆ dom iast0, as ⊆ ∅ ++ adr, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh) ⊦ (rp0 = null ⊃ ¬ dirty0 ∧ P(zh);r = rp0 ∧ zh0 = zh) ∧ (dirty0 → dirty) ∧ (adr ∈ as ↔ ¬ dirty0) ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, true, dirty0, nused), iast1) ∧ nused ≤ # zbrar ∧ # zbrar = BRANCH_SIZE ∧ sorted(zbrar, 0, nused) ∧ payload(zbrar, 0, nused) = payload(zbrar, 0, nused) ∧ ((P * r => mkznode(rp, zbrar, true, dirty0, nused)))(zh0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ ∅ ++ adr ⊆ as ↔ adr ∈ as; (s)% ⊦ ∅ ≠ as ++ adr; (s)% ⊦ #(∅ ++ adr) = 1; (s)%size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%one-size: ⊦ as = ∅ ++ adr → # as = 1; (forward) from specification set-basic[node-store]% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s)% ⊦ adr ∈ ∅ ++ adr0 ↔ adr = adr0; (s)% ⊦ as -- adr = ∅ ↔ as = ∅ ∨ as = ∅ ++ adr; (ws)%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]% ⊦ unmodified(adr, mkznode(rp, zbrar, bv, true, nused), iast); (s)%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]