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Proof step 115 from proof refine-truncate (previous step)

files[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), buf-opt = none, content = files[inode.ino].content, err = ESUCCESS, files0 = files[ino, files[ino].content:= (content[pageno, fill(files[ino].content[pageno], zero, ino1, VFS_PAGE_SIZE - ino1)] upto ino0)], fs = abs-files(files), ino = inode.ino, ino0 = min(n, inode.size), ino1 = inode.size % VFS_PAGE_SIZE, ino4 = 0, ino5 = 0, ino6 = ino4, ino7 = ino5, inode = mkinode(ino2, md0, false, # links(ino2, dirs), 0, m0), new_inode = inode, pageno = m0 / VFS_PAGE_SIZE, root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino2 ∈ files, pageno ∈ files[ino].content, inode.size ≤ n, ino1 + (VFS_PAGE_SIZE - ino1) ≤ # files[ino].content[pageno], VFS_PAGE_SIZE ≥ ino1, psynced → asynced0, pageno ∈ content ∨ buf-opt.some? ⊦ [afs_inode_sync#(new_inode.size:= n; dirs, files0); inode := getinode(inode.ino, dirs, files0); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files0) ∧ afs-cons(dirs, files0) → ⟨posix_truncate#(path, n, user, root, abs-of(of); err1, fs; psynced)⟩ (fs = abs-files(files0) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), VFS_PAGE_SIZE = 0, ino1 = 0, root[path].dir?, ino2 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ m ≤ m; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (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)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)