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Proof step 35 from proof afs-cons-mkdir-ino (previous step)

(ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino]) ;mkdir(# entries0, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries0) ) = mkdir(m7, md3, m8, m9, entries1), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), files[ino0] = mkfile(m1, md1, m3, content), dirs[ino0] = mkdir(# entries0, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries0), afs-cons(dirs, files), ino0 ∈ dirs, m ∈ dirs, ROOT_INO ∈ dirs, # links(ino0, dirs) ≤ 1, ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries0 = ∅, name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, ino ∈ dirs, ino ∈ files, str ∈ entries, (ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅) ∧ m8 = # links(ino0, dirs) ∧ m7 = # entries1 ∧ m9 = # subdirs(ino0, dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino) ∧ (name ∈ entries1 → entries1[name] = ino ∨ entries1[name] ∈ dirs ∨ entries1[name] ∈ files)

User applied rule case distinction

And obtained the following new goals

Proof step 36:
dirs[ino0] = mkdir(# entries0, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries0), files[ino0] = mkfile(m1, md1, m3, content), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), ino0 = m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino]) = mkdir(m7, md3, m8, m9, entries1), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino0 ∈ dirs, # links(ino0, dirs) ≤ 1, name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries0 = ∅, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, str ∈ entries, ino ∈ files, ino ∈ dirs, (ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅) ∧ m8 = # links(ino0, dirs) ∧ m7 = # entries1 ∧ m9 = # subdirs(ino0, dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino) ∧ (name ∈ entries1 → entries1[name] = ino ∨ entries1[name] ∈ dirs ∨ entries1[name] ∈ files)
Proof step 46:
dirs[ino0] = mkdir(# entries0, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries0), files[ino0] = mkfile(m1, md1, m3, content), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), mkdir(# entries0, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries0) = mkdir(m7, md3, m8, m9, entries1), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino0 ∈ dirs, # links(ino0, dirs) ≤ 1, name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries0 = ∅, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, ino0 = m, str ∈ entries, ino ∈ files, ino ∈ dirs, (ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅) ∧ m8 = # links(ino0, dirs) ∧ m7 = # entries1 ∧ m9 = # subdirs(ino0, dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino) ∧ (name ∈ entries1 → entries1[name] = ino ∨ entries1[name] ∈ dirs ∨ entries1[name] ∈ files)

Rule argument

pos: left 1

Proof step 35 from proof afs-cons-mkdir-ino (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information