[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 241 from proof write-prepost-partial (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), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), 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, 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 ∈ files1, m ∈ files, n0 ≤ # buf, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, ⌜buf⌝ to ino to n0 = ⌜buf⌝ to n0, #(⌜buf⌝ to ino) < ⌜n0⌝ , mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 242:
¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m
Proof step 243:
⟨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, files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), 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 ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, n0 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, ⌜buf⌝ to ino to n0 = ⌜buf⌝ to n0, #(⌜buf⌝ to ino) < ⌜n0⌝ , mode ≠ MODE_W ∧ mode ≠ MODE_RW, ¬ # ⌜buf⌝ < ⌜ino⌝ ∧ n0 < ino

Rule argument

spec: stream, inst: buffer-inf name: to-to-ls seq: ¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m subst: [m, n, σ0] → [n0, ino, ⌜buf⌝ ] flags: <all paths>

Additional information

Used terms: n0, ino, ⌜buf⌝