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Proof step 34 from proof afs-cons-inode-sync (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 35:
dirs[ino] = mkdir(# entries0, md1, # links(ino, dirs), # subdirs(ino, dirs), entries0), files[ino] = mkfile(m0, md0, m1, content), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, # links(ino, dirs) ≤ 1, 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 ⊦ # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md]), ino = m, (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs[m, dirs[m].meta:= md]) = ∅ → entries0 = ∅) ∧ (ino ∈ dirs → # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md]) ∧ # links(ino, dirs[m, dirs[m].meta:= md]) ≤ 1) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs[m, dirs[m].meta:= md]))

Rule argument

fma: # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md])

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (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]% ⊦ # ∅ = 0; (s) Used formulas: # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md])