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Proof step 869 from proof inv-renam (previous step)

asynced0 ↔ asynced, dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), dirs0 = dirs, err = ESUCCESS, files0 = files, ino0 = ROOT_INO, p0 = p, user0 = user, dom of < ino2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [vfs_walk#(parent(p), user, dirs, files, asynced; ino0, err)] ( (∃ q, str. p0 = q + str ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino0, dirs0, files0) ∧ px-parent(user0, q, ROOT_INO, dirs0, files0) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs0, files0) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q ∧ ispath(p', ROOT_INO, dirs0, files0) ∧ ¬ px(user0, p', ROOT_INO, dirs0, files0)))) → ⟪inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); if err = ESUCCESS then vfs_may_lookup#(ino0, user, dirs, files, asynced; inode, err); p_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); if err = ESUCCESS then {afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ENOENT then vfs_may_create#(ino0, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then {isdir := false; vfs_may_delete_check#(ino0, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}}; new_inode := inode; new_dent := dent; new_dent_inode := p_inode; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then let dent = new_dent in {old_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); old_dent := mkdentry(str, entries0[str]); old_dent_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced); if dent.dentry? then vfs_put_inode#(new_dent_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), p = ε, entries0[str] ∈ dirs, q + str ' ⊑ p

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 870:
dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), err = ESUCCESS, ino0 = ROOT_INO, p ≠ ε, dom of < ino2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ files, ¬ entries0[str] ∈ dirs, ¬ q + str ' ⊑ p, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [vfs_walk#(parent(p), user, dirs, files, asynced; ino0, err)] ( (∃ q0, str0. p = q0 + str0 ' ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q0, ROOT_INO, ino0, dirs, files) ∧ px-parent(user, q0, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(q0, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q0 ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)))) → ⟪inode := mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0); if err = ESUCCESS then vfs_may_lookup#(ino0, user, dirs, files, asynced; inode, err); p_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); if err = ESUCCESS then {afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ENOENT then vfs_may_create#(ino0, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then {isdir := false; vfs_may_delete_check#(ino0, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}}; new_inode := inode; new_dent := dent; new_dent_inode := p_inode; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then let dent = new_dent in {old_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); old_dent := mkdentry(str, entries0[str]); old_dent_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced); if dent.dentry? then vfs_put_inode#(new_dent_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Rule argument

Additional information

Used simplifier rules: ⊦ p + str = p + str '; (s)