[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 31 from proof truncate-greater (previous step)

VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files[m0] = mkfile(m, md0, # links(m0, dirs), content0), files1 = files [m0, mkfile(m, md0, # links(m0, dirs), content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3) ], inode = mkinode(m0, md, false, # links(m0, dirs), 0, m3), m3 % VFS_PAGE_SIZE ≠ 0, m3 < n, afs-cons(dirs, files), m0 ∈ files, m3 / VFS_PAGE_SIZE ∈ content0 ⊦ [afs_inode_sync#(mkinode(m0, md, false, # links(m0, dirs), 0, n); dirs, files1); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files1[inode.ino].meta, false, files1[inode.ino].nlink, 0, files1[inode.ino].size) ); err := ESUCCESS; asynced := ?] (err = ESUCCESS ⊃ files1[inode.ino].content.stream to files1[inode.ino].size = (files[inode.ino].content.stream to m3) + (σ⊥ to (files1[inode.ino].size - m3)) ∧ inode.ino ∈ files1 ∧ n = files1[inode.ino].size ∧ files[inode.ino].nlink = files1[inode.ino].nlink ∧ files -- inode.ino = files1 -- inode.ino ;⌊err⌋ ∧ files = files1 )

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 32:
VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), files = files1, files1 = files0 [m0, mkfile(m, md0, # links(m0, dirs), content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3) ], inode = mkinode(m0, md, false, # links(m0, dirs), 0, n), inode0 = mkinode(m0, md, false, # links(m0, dirs), 0, m3), m3 < n, afs-cons(dirs, files0), m3 / VFS_PAGE_SIZE ∈ content0, m0 ∈ files0 ⊦ [let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; inode0 := (inode0.ino ∈ dirs ⊃ mkinode(inode0.ino, dirs[inode0.ino].meta, true, dirs[inode0.ino].nlink, dirs[inode0.ino].nsubdirs, dirs[inode0.ino].size) ;mkinode(inode0.ino, files[inode0.ino].meta, false, files[inode0.ino].nlink, 0, files[inode0.ino].size) ); err := ESUCCESS; asynced := ?] (err = ESUCCESS ⊃ files[inode0.ino].content.stream to files[inode0.ino].size = (files0[inode0.ino].content.stream to m3) + (σ⊥ to (files[inode0.ino].size - m3)) ∧ inode0.ino ∈ files ∧ n = files[inode0.ino].size ∧ files0[inode0.ino].nlink = files[inode0.ino].nlink ∧ files0 -- inode0.ino = files -- inode0.ino ;⌊err⌋ ∧ files0 = files ), m3 % VFS_PAGE_SIZE = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_inode_sync#(INODE; DIRS, FILES) {let INO = INODE.ino in if INO ∈ FILES then {FILES[INO].size := INODE.size; FILES[INO].meta := INODE.meta} else if INO ∈ DIRS then DIRS[INO].meta := INODE.meta };