[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 215 from proof write-prepost (previous step)

⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files -- m, files0 -- m = files -- m, files[m] = mkfile(n0 + m0, md, m3, content1), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err2 = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, ((content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0).buf ≠ splice(buf, 0, (content.stream to n0 + m0).buf, m0, n0), n0 ≠ 0, n1 ≠ 0, n0 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 216:
⊦ n1 + m ≤ # buf ∧ m ≠ 0 → splice(buf0, n0, buf, n1, m) = copy(buf0, n0, buf, n1, m)
Proof step 217:
⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files0 -- m = files -- m, files1 -- m = files -- m, of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files[m] = mkfile(n0 + m0, md, m3, content1), buf-opt = none, err2 = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n0 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, m0 + n0 ≤ # (content.stream to n0 + m0).buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ((content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0).buf = copy(buf, 0, (content.stream to n0 + m0).buf, m0, n0), n0 = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: array-splice, inst: buffer name: splice-copy seq: ⊦ n1 + m ≤ # buf ∧ m ≠ 0 → splice(buf0, n0, buf, n1, m) = copy(buf0, n0, buf, n1, m) subst: [m, n1, buf, n0, buf0] → [n0, m0, (content.stream to n0 + m0).buf, 0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ finp(σ0 to m); (s)%finp(σ) ⊦ # σ.buf = (# σ).n; (s)% ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)%n∞ ≠ ∞ ⊦ (⌜m⌝ + n∞).n = m + n∞.n; (s)% ⊦ ⌜m⌝ .n = m; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s) Used terms: n0, m0, (content.stream to n0 + m0).buf, 0, buf