[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 14 from proof refine-writemeta (previous step)

err1 = ESUCCESS, fs = abs-files(files), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ∧ ispath(path, ROOT_INO, ino1, dirs, files) ∧ px-parent(user, path, ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(path, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ path ≠ ε ∧ p' ⊑ parent(path) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ ⟪afs_iget#(ino1, dirs, files, asynced; inode, err1); if err1 = ESUCCESS then if pw(user, inode.meta) then {inode.meta := md; afs_check_commit#(dirs, files; err1; asynced); if err1 = ESUCCESS then afs_write_inode#(inode; err1, dirs, files; asynced)} else err1 := EACCESS⟫ ⟨posix_writemeta#(path, md, user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
⊦ 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)
Proof step 16:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 17:
root[path].dir? ↔ ino1 ∈ dirs, err1 = ESUCCESS, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ ⟪afs_iget#(ino1, dirs, files, asynced; inode, err1); fs := abs-files(files); if err1 = ESUCCESS then if pw(user, inode.meta) then {inode.meta := md; afs_check_commit#(dirs, files; err1; asynced); if err1 = ESUCCESS then afs_write_inode#(inode; err1, dirs, files; asynced)} else err1 := EACCESS⟫ ⟨posix_writemeta#(path, md, user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)

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));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)% ⊦ ESUCCESS ≠ EACCESS; (s)% ⊦ ESUCCESS ≠ ENOENT; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)