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Proof step 8 from proof btree-null-or-clean-below (previous step)

zh0[r] = mkznode(r0, zbrar, boolvar, false, m) ⊦ (∃ zbrar0, dirty0, nused. (dirty0 → dirty) ∧ (adr ∈ as ↔ ¬ dirty0) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar0, height = 0, dirty0, nused), iast) ∧ (( r => mkznode(rp, zbrar0, height = 0, dirty0, nused) * bnode(r, zbrar0, 0, nused, nused, height, dirty0, ri, iast, as -- adr, alladrs -- adr) * P) )(zh0)) ↔ adr ∈ as ∧ adr ∈ alladrs ∧ (∃ zbrar0, nused. nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar0, height = 0, false, nused), iast) ∧ (( r => mkznode(rp, zbrar0, height = 0, false, nused) * bnode(r, zbrar0, 0, nused, nused, height, false, ri, iast, as -- adr, alladrs -- adr) * P) )(zh0)), r = null

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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