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Proof step 114 from proof afs-cons-rename-file-dentry (previous step)

# links(entries0[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0);mkdir(m4, md6, # links(m, dirs0), m8, entries0)) = mkdir(m6, md5, m9, m10, entries), (ino = m ⊃ (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 ;(ino = m0 ⊃ mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0) ;mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2) ) ) = mkdir(m19, md10, m20, m21, entries3), files0[ino] = mkfile(m12, md7, m13, content0), dirs0[m] = mkdir(m4, md6, # links(m, dirs0), m8, entries0), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), afs-cons(dirs0, files0), ino ∈ dirs0, m ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files0, str ∈ entries0, m0 ∈ dirs0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, m = m0 → md1 = md2, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m0 = m, m20 = # links (ino, dirs0[m0, mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0).meta:= md2] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 ]), entries1[str0] ∈ dirs0, entries0[str] ∈ dirs0, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 115:
# links(entries[str], dirs0) = m11 + 1, (ino = m ⊃ mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ;(ino = m0 ⊃ mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0) ;mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2) ) ) = mkdir(m19, md10, m20, m21, entries3), files0[ino] = mkfile(m12, md7, m13, content0), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), afs-cons(dirs0, files0), ino ∈ dirs0, m ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files0, str ∈ entries, m0 ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m0 = m, m20 = # links (ino, dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)] [m, mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ]), entries1[str0] ∈ dirs0, entries[str] ∈ dirs0

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)