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Proof step 206 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), files = files0[ino2, mkfile(m0, md0, # links(ino2, dirs), content0 upto min(n, m0))], inode = mkinode(ino2, md0, false, # links(ino2, dirs), 0, m0), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ROOT_INO ∈ dirs, ino2 ∈ files0, ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ [afs_inode_sync#(mkinode(ino2, md0, false, # links(ino2, dirs), 0, n); dirs, files); 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, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨fs := abs-files(files0); posix_truncate#(path, n, user, root, abs-of(of); err1, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 207:
files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), files = files0[ino2, mkfile(m0, md0, # links(ino2, dirs), content0 upto min(n, m0))], inode = mkinode(ino2, md0, false, # links(ino2, dirs), 0, n), inode0 = mkinode(ino2, md0, false, # links(ino2, dirs), 0, m0), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ino2 ∈ files0, ROOT_INO ∈ dirs, psynced → asynced0 ⊦ [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 := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨fs := abs-files(files0); posix_truncate#(path, n, user, root, abs-of(of); err1, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), root[path].dir?, ino2 ∈ dirs, m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

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 };