[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 20 from proof btree-refed-subseteq-alladrs (previous step)

# zbrar = BRANCH_SIZE, # asar = m + 1, # asar0 = m + 1, adr ∈ as ↔ ¬ dirty0, union(asar, 0, m + 1) = as -- adr, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r0, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, fi), iast, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r0 => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0), m < BRANCH_SIZE, disj(asar, 0, m + 1), disj(asar0, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), unmodified(adr, mkznode(rp, zbrar, false, dirty0, m + 1), iast), dirty0 → dirty, (r = null ⊃ adr ∈ as ∧ P(zh);r0 = r ∧ zh0 = zh), ∀ rp, r, adr, dirty, fi, iast, as, alladrs, nstat, P, zh. ((btree(rp, r, adr, height0, dirty, fi, iast, as, alladrs, nstat) * P))(zh) → as ⊆ alladrs ⊦ adr ∈ union(asar0, 0, m + 1), as ⊆ union(asar0, 0, m + 1), as ⊆ union(asar0, 0, m + 1) ++ adr

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-union, inst: node-store name: delete-shift seq: ⊦ adr ∈ as → (as -- adr = as0 ↔ as = as0 ++ adr ∧ ¬ adr ∈ as0) subst: [adr, as, as0] → [adr, as, union(asar, 0, m + 1)] flags: <all paths>

Additional information

Used terms: adr, as, union(asar, 0, m + 1)