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Proof step 36 from proof inv-evict (previous step)

0 = m3, files[ino] = mkfile(m, md, m0, content), files[m1] = mkfile(m2, md0, m3, content0), afs-cons(dirs, files), m1 ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ m1 ∈ dirs, (ino ≠ m1 ∧ ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ≠ m1 ∧ dirs[ino].entries[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# links(m1, dirs) = 0, files[ino] = mkfile(m, md, m0, content), files[m1] = mkfile(m2, md0, 0, content0), afs-cons(dirs, files), m1 ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ m1 ∈ dirs, (ino ≠ m1 ∧ ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ≠ m1 ∧ dirs[ino].entries[name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%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