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Proof step 21 from proof btree-write-other (previous step)

∀ rp, r, adr0, dirty, ri, iast, adr, ind, as, alladrs, nstat, P, zh. ( ((btree(rp, r, adr0, height0, dirty, ri, iast[adr, ind], as, alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr0, height0, dirty, ri, iast, as, alladrs, nstat) * P))(zh)) ∨ adr ∈ as ⊦ (∃ r0, zh0, zbrar, dirty0, nused. (r = null ⊃ ¬ dirty0 ∧ P(zh);r0 = r ∧ zh0 = zh) ∧ (dirty0 → dirty) ∧ (adr0 ∈ as ↔ ¬ dirty0) ∧ adr0 ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr0, mkznode(rp, zbrar, false, dirty0, nused), iast[adr, ind]) ∧ (( r0 => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast[adr, ind], as -- adr0, alladrs -- adr0) * P) )(zh0)) ↔ (∃ r0, zh0, zbrar, dirty0, nused. (r = null ⊃ ¬ dirty0 ∧ P(zh);r0 = r ∧ zh0 = zh) ∧ (dirty0 → dirty) ∧ (adr0 ∈ as ↔ ¬ dirty0) ∧ adr0 ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr0, mkznode(rp, zbrar, false, dirty0, nused), iast) ∧ (( r0 => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast, as -- adr0, alladrs -- adr0) * P) )(zh0)), adr ∈ as

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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