[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 8 from proof crash-neutral-lookup (previous step)

dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), afs-cons(dirs, files), p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨if dent.name ∈ entries then {dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ true, ⟨fail#(; ; err)⟩ true

Heuristic conditional right split applied rule if right

And obtained the following new goals

Proof step 9:
dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), afs-cons(dirs, files), dent.name ∈ entries, p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS⟩ true, ⟨fail#(; ; err)⟩ true
Proof step 11:
dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), afs-cons(dirs, files), p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨dent := negdentry(dent.name); err := ENOENT⟩ true, ⟨fail#(; ; err)⟩ true, dent.name ∈ entries

Rule argument

pos: right 1

Proof step 8 from proof crash-neutral-lookup (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

Additional information