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Proof step 7 from proof btree-null-or-clean-below (previous step)

zh0[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), r = null ∨ ¬ boolvar0 ⊦ (∃ r1, zh, zbrar, dirty1, nused. (r = null ⊃ ¬ dirty1 ∧ P(zh0);r1 = r ∧ zh = zh0) ∧ (dirty1 → dirty) ∧ (adr ∈ as ↔ ¬ dirty1) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, height = 0, dirty1, nused), iast) ∧ (( r1 => mkznode(rp, zbrar, height = 0, dirty1, nused) * bnode(r1, zbrar, 0, nused, nused, height, dirty1, ri, iast, as -- adr, alladrs -- adr) * P) )(zh)) ↔ (∃ r1, zh, zbrar, dirty, nused. (r = null ⊃ ¬ dirty ∧ P(zh0);r1 = r ∧ zh = zh0) ∧ (dirty → false) ∧ (adr ∈ as ↔ ¬ dirty) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, height = 0, dirty, nused), iast) ∧ (( r1 => mkznode(rp, zbrar, height = 0, dirty, nused) * bnode(r1, zbrar, 0, nused, nused, height, dirty, ri, iast, as -- adr, alladrs -- adr) * P) )(zh))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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

Rule argument

Additional information

Used simplifier rules: sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]