[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 219 from proof truncate-inv (previous step)

⟨afs_inode_sync#(mkinode(ino4, md, false, # links(ino4, dirs), 0, m0); dirs, files1)⟩ (dirs = dirs0 ∧ files1 = files0), files0[ino4] = mkfile(m, md0, m1, content1), files[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), files1 = files[ino4, mkfile(m0, md, # links(ino4, dirs), content0 upto m0)], files -- ino4 ≠ files0 -- ino4, afs-cons(dirs, files), afs-cons(dirs0, files0), files ~ files0, ino4 ∈ files ⊦ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

Heuristic unfold applied rule call left

And obtained the following new goals

Proof step 220:
⟨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⟩ (dirs = dirs0 ∧ files = files0), files2[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), files0[ino4] = mkfile(m, md0, m1, content1), files = files1, files1 = files2[ino4, mkfile(m0, md, # links(ino4, dirs), content0 upto m0)], inode = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0), afs-cons(dirs0, files0), afs-cons(dirs, files2), files2 ~ files0, ino4 ∈ files2 ⊦ files2 -- ino4 = files0 -- ino4, m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

Rule argument

pos: left 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 };