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Proof step 37 from proof inv-mkdir (previous step)

dent = negdentry((q + str ').last), err = ESUCCESS, err0 = ESUCCESS, ino = ino0, inode = getinode(ino, dirs, files), inode.directory, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), pw(user, inode.meta), px(user, inode.meta), px-parent(user, q, ROOT_INO, dirs, files) ⊦ ⟪afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {dent := negdentry((q + str ').last); afs_mkdir#(md; inode, c_inode, dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), q + str ' = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
dent = negdentry(str), err = ESUCCESS, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, dirs[ino0].meta), px(user, dirs[ino0].meta), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ ⟪afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); afs_mkdir#(md; inode, c_inode, dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

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)% ⊦ 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)% ⊦ p + str ' ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ (p + str ').last = str; (s)