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Proof step 7 from proof btree-imp-dirty (previous step)

∃ r1, zh1, zbrar, dirty1, nused. (r = null ⊃ ¬ dirty1 ∧ P(zh);r1 = r ∧ zh1 = zh) ∧ (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, fi, iast, as -- adr, alladrs -- adr) * P) )(zh1) ⊦ ∃ r0, zh0, zbrar, dirty0, nused. (r = null ⊃ ¬ dirty0 ∧ P(zh);r0 = r ∧ zh0 = zh) ∧ (adr ∈ as ↔ ¬ dirty0) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, height = 0, dirty0, nused), iast) ∧ (( r0 => mkznode(rp, zbrar, height = 0, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height, dirty0, fi, iast, as -- adr, alladrs -- adr) * P) )(zh0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
adr ∈ as ↔ ¬ dirty0, ((r0 => mkznode(rp, zbrar, height = 0, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height, dirty0, fi, iast, as -- adr, alladrs -- adr) * P) )(zh0), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, height = 0, dirty0, nused), iast), adr ∈ alladrs, dirty0 → dirty, (r = null ⊃ adr ∈ as ∧ P(zh);r0 = r ∧ zh0 = zh) ⊦ # alladrs = 0, alladrs = ∅, ∃ r1, zh1, zbrar0, dirty1, nused0. (r = null ⊃ ¬ dirty1 ∧ P(zh);r1 = r ∧ zh1 = zh) ∧ (adr ∈ as ↔ ¬ dirty1) ∧ nsize(nused0, nstat) ∧ unmodified(adr, mkznode(rp, zbrar0, height = 0, dirty1, nused0), iast) ∧ (( r1 => mkznode(rp, zbrar0, height = 0, dirty1, nused0) * bnode(r1, zbrar0, 0, nused0, nused0, height, dirty1, fi, iast, as -- adr, alladrs -- adr) * P) )(zh1)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]