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Proof step 17 from proof valid-parent-ino-precond (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
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, fs[ri[inodekey(m)]].nlink = 0, ro = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)