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Proof step 12 from proof btree-inv-format (previous step)

⊦ (( btree (null, null, @(n, m0, m1), 0, false, ∅, nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), ∅ ++ @(n, m0, m1), ∅ ++ @(n, m0, m1), ok) * true) )(zh)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ((btree(rp, r0, adr, height, dirty0, ri, iast, as, alladrs, nstat) * P))(zh0) ↔ (∃ r, zh, zbrar, dirty, nused. (r0 = null ⊃ ¬ dirty ∧ P(zh0);r = r0 ∧ zh = zh0) ∧ (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) * P) )(zh))
Proof step 14:
⊦ ∃ r, zh1, zbrar, dirty, nused. (null = null ⊃ ¬ dirty ∧ true(zh);r = null ∧ zh1 = zh) ∧ (dirty → false) ∧ (@(n, m0, m1) ∈ ∅ ++ @(n, m0, m1) ↔ ¬ dirty) ∧ @(n, m0, m1) ∈ ∅ ++ @(n, m0, m1) ∧ nsize(nused, ok) ∧ unmodified (@(n, m0, m1), mkznode(null, zbrar, 0 = 0, dirty, nused), nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])) ∧ (( r => mkznode(null, zbrar, 0 = 0, dirty, nused) * bnode (r, zbrar, 0, nused, nused, 0, dirty, ∅, nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), (∅ ++ @(n, m0, m1)) -- @(n, m0, m1), (∅ ++ @(n, m0, m1)) -- @(n, m0, m1)) * true) )(zh1)

Rule argument

spec: <toplevel> name: btree seq: ⊦ (( btree (rp, r0, adr, height, dirty0, ri, iast, as, alladrs, nstat) * P) )(zh0) ↔ (∃ r, zh, zbrar, dirty, nused. (r0 = null ⊃ ¬ dirty ∧ P(zh0);r = r0 ∧ zh = zh0) ∧ (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) * P) )(zh)) subst: [zh0, P, nstat, alladrs, as, iast, ri, dirty0, height, adr, r0, rp] → [zh, true, ok, ∅ ++ @(n, m0, m1), ∅ ++ @(n, m0, m1), nodes ((∅ )[n, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1) ]), ∅, false, 0, @(n, m0, m1), null, null] flags: <all paths>

Additional information

Used terms: zh, true, ok, ∅ ++ @(n, m0, m1), ∅ ++ @(n, m0, m1), nodes ((∅ )[n, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1) ]), ∅, false, 0, @(n, m0, m1), null, null