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Proof step 30 from proof afs-cons-inode-sync (previous step)

dirs[ino] = mkdir(m5, md1, m6, m7, entries0), files[ino] = mkfile(m0, md0, m1, content), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries0 = ∅, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files ⊦ ino = m, ino ∈ dirs, (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs[m, dirs[m].meta:= md]) = ∅ → entries0 = ∅) ∧ ( ino ∈ dirs → m6 = # links(ino, dirs[m, dirs[m].meta:= md]) ∧ # links(ino, dirs[m, dirs[m].meta:= md]) ≤ 1 ∧ m5 = # entries0 ∧ m7 = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs[m, dirs[m].meta:= md]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
dirs[ino] = mkdir(m5, md1, m6, m7, entries0), files[ino] = mkfile(m0, md0, # links(ino, dirs), content), afs-cons(dirs, files), ino ∈ files, m ∈ dirs, ROOT_INO ∈ dirs ⊦ # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md]), ino ∈ dirs

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