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Proof step 28 from proof btree-istore-reduce-refed (previous step)

((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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ unmodified(adr, znd, iast) ↔ ¬ znd.dirty → adr ∈ iast ∧ iast[adr] = save(znd)
Proof step 30:
((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), adr ∈ iast0, adr ∈ alladrs, adr ∈ as, as ⊆ alladrs, as ⊆ dom iast0, iast0 | as ⊆ iast1, ¬ mkznode(rp, zbrar, false, false, nused).dirty → adr ∈ iast0 ∧ iast0[adr] = save(mkznode(rp, zbrar, false, false, nused)), (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) ⊦ # as = 0, # alladrs = 0, alladrs = ∅, as = ∅, unmodified(adr, mkznode(rp, zbrar, false, false, nused), iast1)

Rule argument

spec: zbranch-array-ops name: unmodified seq: ⊦ unmodified(adr, znd, iast) ↔ ¬ znd.dirty → adr ∈ iast ∧ iast[adr] = save(znd) subst: [iast, znd, adr] → [iast0, mkznode(rp, zbrar, false, false, nused), adr] flags: <all paths>

Additional information

Used terms: iast0, mkznode(rp, zbrar, false, false, nused), adr