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Proof step 51 from proof refine-rmdir (previous step)

abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri)[str] = (∅)[str], fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fo.inodes?, orphans(fs, ri).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(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, inodekey(m) ∈ ri, asynced → boolvar, ∀ str0. ¬ dentrykey(fs[ri[dentrykey(m, str)]].ino, str0) ∈ ri ∧ abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri)[str0] = (∅)[str0], links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ # dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = 0, fs[ri[dentrykey(m, str)]].ino = ROOT_INO, dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅, dentrykey(fs[ri[dentrykey(m, str)]].ino, str) ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [∅, dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri)] flags: <all paths>

Additional information

Used terms: ∅, dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri)