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Proof step 96 from proof afs-cons-rename-dir-negdentry (previous step)

(entries2[str] = ino ⊃ (links(entries2[str], dirs0) -- mklink(m, str)) ++ mklink(m0, str0);links(ino, dirs0)) = ∅, (ino = m0 ⊃ mkdir(m4 + 1, md1, # links(m0, dirs0), m7 + 1, entries0[str0, entries2[str]]) ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), files[ino] = mkfile(m9, md2, m11, content), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), afs-cons(dirs0, files), m0 ∈ dirs0, ino ∈ dirs0, ROOT_INO ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, m ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(ino, dirs0) = ∅ → entries = ∅, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries2[str] = ino, entries4 = ∅, ino = ROOT_INO, m0 = m, str0 ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
# links(ino, dirs0) = 0, (ino = m0 ⊃ mkdir(m4 + 1, md1, # links(m0, dirs0), m7 + 1, entries0[str0, entries2[str]]) ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(0, md6, 0, # subdirs(ino, dirs0), ∅)) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), files[ino] = mkfile(m9, md2, m11, content), dirs0[ino] = mkdir(0, md6, 0, # subdirs(ino, dirs0), ∅), afs-cons(dirs0, files), m0 ∈ dirs0, ino ∈ dirs0, ROOT_INO ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, m ∈ dirs0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries2[str] = ino, entries4 = ∅, ino = ROOT_INO, m0 = m, str0 ∈ entries0

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 0; (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)