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Proof step 31 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n0 + n % VFS_PAGE_SIZE, files[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), files0 = files [ino0, mkfile(m, md0, # links(ino0, dirs), content0[n / VFS_PAGE_SIZE, fill(content0[n / VFS_PAGE_SIZE], zero, n % VFS_PAGE_SIZE, n0)] upto n) ], inode = mkinode(ino0, md1, false, # links(ino0, dirs), 0, n), n % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files), ino0 ∈ files, n / VFS_PAGE_SIZE ∈ content0 ⊦ [afs_inode_sync#(mkinode(ino0, md1, false, # links(ino0, dirs), 0, n); dirs, files0); 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, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ); err := ESUCCESS; asynced := ?] (err = ESUCCESS → files0[ino0].content.stream from n = σ⊥)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 32:
VFS_PAGE_SIZE = n0 + n % VFS_PAGE_SIZE, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), files = files0, files0 = files1 [ino0, mkfile(m, md0, # links(ino0, dirs), content0[n / VFS_PAGE_SIZE, fill(content0[n / VFS_PAGE_SIZE], zero, n % VFS_PAGE_SIZE, n0)] upto n) ], inode = mkinode(ino0, md1, false, # links(ino0, dirs), 0, n), inode0 = mkinode(ino0, md1, false, # links(ino0, dirs), 0, n), afs-cons(dirs, files1), n / VFS_PAGE_SIZE ∈ content0, ino0 ∈ files1 ⊦ [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[ino0].content.stream from n = σ⊥), n % 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 };