[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 32 from proof walk-term (previous step)

err = EACCESS, err0 = ESUCCESS, err1 = ESUCCESS, getinode(ino, dirs, files).directory, afs-cons(dirs, files), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ino ∈ dirs ∨ ino ∈ files, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ ⟪while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}⟫ true, p = ε, px(user, getinode(ino, dirs, files).meta)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
err = EACCESS, p ≠ ε, afs-cons(dirs, files), ino ∈ dirs, ¬ px(user, dirs[ino].meta), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ ⟪while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}⟫ true

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (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)