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Proof step 27 from proof btree-istore-reduce-refed (previous step)

adr ∈ as ↔ ¬ dirty0, ((r => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast0, as -- adr, alladrs -- adr) * P) )(zh0), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, false, dirty0, nused), iast0), adr ∈ alladrs, as ⊆ alladrs, as ⊆ dom iast0, iast0 | as ⊆ iast1, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh), ∀ rp, rp0, adr, dirty, ri, iast0, as, alladrs, nstat, P, zh, iast1. ((btree(rp, rp0, adr, height0, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) ∧ iast0 | as ⊆ iast1 ∧ as ⊆ dom iast0 ∧ as ⊆ alladrs → ((btree(rp, rp0, adr, height0, dirty, ri, iast1, as, alladrs, nstat) * P))(zh) ⊦ # alladrs = 0, alladrs = ∅, unmodified(adr, mkznode(rp, zbrar, false, dirty0, nused), iast1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
((r => mkznode(rp, zbrar, false, false, nused) * bnode(r, zbrar, 0, nused, nused, height0 + 1, false, ri, iast0, as -- adr, alladrs -- adr) * P) )(zh0), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, false, false, nused), iast0), adr ∈ as, adr ∈ alladrs, adr ∈ iast0, iast0 | as ⊆ iast1, as ⊆ dom iast0, as ⊆ alladrs, (rp0 = null ⊃ P(zh);r = rp0 ∧ zh0 = zh), ∀ rp, rp0, adr, dirty, ri, iast0, as, alladrs, nstat, P, zh, iast1. ((btree(rp, rp0, adr, height0, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) ∧ iast0 | as ⊆ iast1 ∧ as ⊆ dom iast0 ∧ as ⊆ alladrs → ((btree(rp, rp0, adr, height0, dirty, ri, iast1, as, alladrs, nstat) * P))(zh) ⊦ # alladrs = 0, # as = 0, alladrs = ∅, as = ∅, unmodified(adr, mkznode(rp, zbrar, false, false, nused), iast1)

Rule argument

Additional information

Used simplifier rules: 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]% ⊦ unmodified(adr, mkznode(rp, zbrar, bv, true, nused), iast); (s)