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Proof step 16 from proof refine-truncate (previous step)

isdir ↔ false, 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)), 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) ⊦ [vfs_may_open#(ino1, isdir, MODE_W, user, dirs, files, asynced; inode, err1); if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); pageno := 0; if err1 = ESUCCESS then pageno := inode.size / VFS_PAGE_SIZE; fs := abs-files(files); if err1 = ESUCCESS then {buf-opt := none; afs_truncate#(n, pageno; buf-opt, inode, isdir0, err1, dirs, files, asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_truncate#(path, n, user, root, abs-of(of); err0, 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 17:
⊦ 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 18:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 19:
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 ⊦ [vfs_may_open#(ino1, false, MODE_W, user, dirs, files, asynced; inode, err1); if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); pageno := 0; if err1 = ESUCCESS then pageno := inode.size / VFS_PAGE_SIZE; fs := abs-files(files); if err1 = ESUCCESS then {buf-opt := none; afs_truncate#(n, pageno; buf-opt, inode, isdir0, err1, dirs, files, asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_truncate#(path, n, user, root, abs-of(of); err0, 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)