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Proof step 19 from proof refine-readmeta (previous step)

err1 = ESUCCESS, ino0 = ino3, ino1 = ino4, md = md0, root.dir?, dom of < ino6, 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, ino2, 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#(ino2, dirs, files, asynced; inode, err1); if err1 = ESUCCESS then if pr(user, inode.meta) then {md := inode.meta, ino0 := inode.size; if inode.directory then ino1 := inode.nsubdirs + 2 else ino1 := inode.nlink} else err1 := EACCESS] ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ md = md0 ∧ ino1 = ino4 ∧ ino0 = ino3 ∧ err1 = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
⊦ 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 21:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 22:
root[path].dir? ↔ ino2 ∈ dirs, err1 = ESUCCESS, root.dir?, dom of < ino6, 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), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ [afs_iget#(ino2, dirs, files, asynced; inode, err1); md := md0; ino1 := ino4; ino0 := ino3; if err1 = ESUCCESS then if pr(user, inode.meta) then {md := inode.meta, ino0 := inode.size; if inode.directory then ino1 := inode.nsubdirs + 2 else ino1 := inode.nlink} else err1 := EACCESS] ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ md = md0 ∧ ino1 = ino4 ∧ ino0 = ino3 ∧ 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)