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Proof step 59 from proof refine-rmdir (previous step)

abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[inodekey(m)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[dentrykey(m, str)]].ino = ROOT_INO, 1 ≤ fs[ri[inodekey(m)]].nsubdirs

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: afs-cons-abs-dir-subdirs seq: ⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ∧ ino ∈ abs-dirs(fs, ri) ∧ subdirs(ino, abs-dirs(fs, ri)) ≠ ∅ → fs[ri[inodekey(ino)]].nsubdirs ≥ 1 subst: [fs, ri, ino] → [fs, ri, m]

Additional information

Used terms: fs, ri, m