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Proof step 22 from proof afs-cons-inode-sync (previous step)

files[ino] = mkfile(m0, md0, m1, content), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ files ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # 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 = ∅ ⊦ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs[m, dirs[m].meta:= md]) = ∅ → (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries = ∅) ∧ ( ino ∈ dirs → (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).nlink = # links(ino, dirs[m, dirs[m].meta:= md]) ∧ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).nlink ≤ 1 ∧ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).size = # (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries ∧ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).nsubdirs = # subdirs(ino, dirs[m, dirs[m].meta:= md])) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs[m, dirs[m].meta:= md])) ∧ ( ino ∈ dirs ∧ name ∈ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries → (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries[name] ∈ dirs ∨ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
files[ino] = mkfile(m0, md0, m1, content), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, 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 ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files ⊦ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs[m, dirs[m].meta:= md]) = ∅ → (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries = ∅) ∧ ( ino ∈ dirs → (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).nlink = # links(ino, dirs[m, dirs[m].meta:= md]) ∧ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).nlink ≤ 1 ∧ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).size = # (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries ∧ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).nsubdirs = # subdirs(ino, dirs[m, dirs[m].meta:= md])) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs[m, dirs[m].meta:= md])) ∧ ( ino ∈ dirs ∧ name ∈ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries → (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries[name] ∈ dirs ∨ (ino = m ⊃ dirs[m].meta:= md;dirs[ino]).entries[name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)