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Proof step 8 from proof btree-null (previous step)

((r => mkznode(rp, zbrar, height = 0, false, nused) * bnode(r, zbrar, 0, nused, nused, height, false, ri, iast, as -- adr, alladrs -- adr) * true) )(zh), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, height = 0, false, nused), iast), adr ∈ iast, adr ∈ alladrs, adr ∈ as, as ⊆ dom iast, as ⊆ alladrs ⊦ # alladrs = 0, # as = 0, alladrs = ∅, as = ∅, ∃ r, zh, zbrar, dirty, nused. (null = null ⊃ ¬ dirty ∧ true(zh1);r = null ∧ zh = zh1) ∧ (dirty → dirty0) ∧ (adr ∈ as ↔ ¬ dirty) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, height = 0, dirty, nused), iast) ∧ (( r => mkznode(rp, zbrar, height = 0, dirty, nused) * bnode(r, zbrar, 0, nused, nused, height, dirty, ri, iast, as -- adr, alladrs -- adr) * true) )(zh)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
((r => mkznode(rp, zbrar, height = 0, false, nused) * bnode(r, zbrar, 0, nused, nused, height, false, ri, iast, as -- adr, alladrs -- adr) * true) )(zh), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, height = 0, false, nused), iast), adr ∈ as, adr ∈ alladrs, adr ∈ iast, as ⊆ alladrs, as ⊆ dom iast ⊦ # as = 0, # alladrs = 0, alladrs = ∅, as = ∅, ∃ r0, zh0, zbrar0, nused0. nsize(nused0, nstat) ∧ unmodified(adr, mkznode(rp, zbrar0, height = 0, false, nused0), iast) ∧ (( r0 => mkznode(rp, zbrar0, height = 0, false, nused0) * bnode(r0, zbrar0, 0, nused0, nused0, height, false, ri, iast, as -- adr, alladrs -- adr) * true) )(zh0)

Rule argument

Additional information

Used simplifier rules: ⊦ true(zh); (s)