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Proof step 15 from proof valid-parent-ino-precond (previous step)

fs[ri[inodekey(m)]].directory, ro.inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), log-cons(log, fs), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m) ∈ ri, inodekey(m) ∈ ro, ∀ ino. inodekey(ino) ∈ ro ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ # links(m, abs-dirs(fs, ri)) = 0, # ro = 0, links(m, abs-dirs(fs, ri)) = ∅, ro = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ afs-cons(dirs, files) → (links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0))
Proof step 17:
fs[ri[inodekey(m)]].directory, fo.inodes?, ro.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), log-cons(log, fs), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m) ∈ ro, inodekey(m) ∈ ri, ∀ ino. inodekey(ino) ∈ ro ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ # ro = 0, # links(m, abs-dirs(fs, ri)) = 0, ro = ∅, (m ∈ abs-dirs(fs, ri) → abs-dirs(fs, ri)[m].nlink = 0) ∧ (m ∈ abs-files(fs, ri) → abs-files(fs, ri)[m].nlink = 0)

Rule argument

spec: afs-base name: afs-cons-links-empty seq: ⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)) subst: [files, dirs, ino] → [abs-files(fs, ri), abs-dirs(fs, ri), m] flags: <all paths>

Additional information

Used terms: abs-files(fs, ri), abs-dirs(fs, ri), m