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Proof step 28 from proof truncate-empty (previous step)

files[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), buf-opt = none, content = files[inode.ino].content, files0 = files[ino, files[ino].content:= (content[pageno, fill(files[ino].content[pageno], zero, old_ino0, VFS_PAGE_SIZE - old_ino0)] upto old_ino)], ino = inode.ino, inode = mkinode(ino0, md1, false, # links(ino0, dirs), 0, n), new_inode = inode, old_ino = min(n, inode.size), old_ino0 = inode.size % VFS_PAGE_SIZE, old_ino1 = 0, old_ino2 = 0, pageno = n / VFS_PAGE_SIZE, afs-cons(dirs, files), ino0 ∈ files, pageno ∈ files[ino].content, inode.size ≤ n, old_ino0 + (VFS_PAGE_SIZE - old_ino0) ≤ # files[ino].content[pageno], VFS_PAGE_SIZE ≥ old_ino0, pageno ∈ content ∨ buf-opt.some? ⊦ [afs_inode_sync#(new_inode.size:= n; dirs, files0); inode := getinode(inode.ino, dirs, files0); err := ESUCCESS; asynced := ?] (err = ESUCCESS → files0[ino0].content.stream from n = σ⊥), VFS_PAGE_SIZE = 0, old_ino0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
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, VFS_PAGE_SIZE - n % VFS_PAGE_SIZE)] 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⊥)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2).size:= m6 = mkinode(m, md, boolvar, m0, m1, m6); (s)% ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ min(n, n) = n; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)