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Proof step 67 from proof refine-readdir (previous step)

isdir ↔ true, root[path].dir? ↔ ino1 ∈ dirs, inode.directory ↔ isdir, err = ESUCCESS, err1 = err, err2 = err3, err3 = ESUCCESS, ino = ino1, inode = getinode(ino, dirs, files), mode = MODE_R, strings = strings0, 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), pre-iget(ino, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ [afs_readdir#(inode, dirs, files, asynced; strings, err1)] ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ err1 = err0), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, inode.meta), (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, inode.meta)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
err = ESUCCESS, strings = strings0, root.dir?, root[path].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), pr(user, dirs[ino1].meta), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ [afs_readdir#(mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), dirs, files, asynced; strings, err)] ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ MODE_R ≠ MODE_RW; (s)% ⊦ MODE_R ≠ MODE_W; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (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)