[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-inv-format (previous step)

⊦ r = null, unmodified (@(n, m0, m1), mkznode(null, mkzbrarray(BRANCH_SIZE), true, false, 0), nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])) ∧ ((true * r => mkznode(null, mkzbrarray(BRANCH_SIZE), true, false, 0)))((∅ ++ r)[r, mkznode(null, mkzbrarray(BRANCH_SIZE), true, false, 0)])

User applied rule case distinction

And obtained the following new goals

Proof step 21:
⊦ r = null, unmodified (@(n, m0, m1), mkznode(null, mkzbrarray(BRANCH_SIZE), true, false, 0), nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]))

Rule argument

pos: right 2

Additional information

Used simplifier rules: in-emp: ⊦ ¬ r ∈ ∅; from specification heap[zheap]%in-alloc: r0 ≠ null, ¬ r0 ∈ zh ⊦ r ∈ zh ++ r0 ↔ ¬ ¬(r = r0 ∨ r ∈ zh); from specification heap[zheap]%map-putex-simp: r ∈ zh ⊦ ¬ ((r => znd * P0))(zh[r, znd0]) ↔ ¬(znd = znd0 ∧ ((r =>_ * P0))(zh)); from specification maplet[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%mapex-new-rw: ¬ r ∈ zh, r ≠ null ⊦ ¬ ((r =>_ * P0))(zh ++ r) ↔ ¬ P0(zh); from specification maplet[zheap]%trueH: ⊦ true(zh); from specification heap-sep[zheap]