[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 193 from proof refine-read (previous step)

files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf1, 0, dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf0, 0, dirs, files), fd ∈ of, m ∈ files, n0 ≤ # buf0, m0 ≤ m1, psynced → asynced ⊦ buf1 = buf0, mode ≠ MODE_R ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 194:
⊦ read-inv(n0, n1, inode, buf0, buf1, n, dirs, files) ↔ afs-cons(dirs, files) ∧ # buf0 = # buf1 ∧ inode.ino ∈ files ∧ files[inode.ino].size = inode.size ∧ n0 + n ≤ n1 ∧ n0 + n ≤ inode.size ∧ n1 - n0 ≤ # buf0 ∧ read-inv(n0, n1, buf0, buf1, n, files[inode.ino].content)
Proof step 195:
# buf0 = # buf1, files[mkinode(m, md, false, # links(m, dirs), 0, m1).ino].size = mkinode(m, md, false, # links(m, dirs), 0, m1).size, of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf0, 0, dirs, files), read-inv(m0, m0 + n0, buf0, buf1, 0, files[mkinode(m, md, false, # links(m, dirs), 0, m1).ino].content), m ∈ files, fd ∈ of, mkinode(m, md, false, # links(m, dirs), 0, m1).ino ∈ files, m0 ≤ m1, n0 ≤ # buf0, m0 + 0 ≤ m0 + n0, m0 + 0 ≤ mkinode(m, md, false, # links(m, dirs), 0, m1).size, m0 + n0 - m0 ≤ # buf0, psynced → asynced ⊦ buf1 = buf0, mode ≠ MODE_R ∧ mode ≠ MODE_RW

Rule argument

spec: vfs-contracts name: read-inv-strong seq: ⊦ read-inv(n0, n1, inode, buf0, buf1, n, dirs, files) ↔ afs-cons(dirs, files) ∧ # buf0 = # buf1 ∧ inode.ino ∈ files ∧ files[inode.ino].size = inode.size ∧ n0 + n ≤ n1 ∧ n0 + n ≤ inode.size ∧ n1 - n0 ≤ # buf0 ∧ read-inv(n0, n1, buf0, buf1, n, files[inode.ino].content) subst: [files, dirs, n, buf1, buf0, inode, n1, n0] → [files, dirs, 0, buf1, buf0, mkinode(m, md, false, # links(m, dirs), 0, m1), m0 + n0, m0] flags: <all paths>

Additional information

Used terms: files, dirs, 0, buf1, buf0, mkinode(m, md, false, # links(m, dirs), 0, m1), m0 + n0, m0