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Proof step 54 from proof refine-rmdir (previous step)

key.ino = fs[ri[dentrykey(m, str)]].ino, abs-children(key.ino, fs, ri)[str] = (∅)[str], key.dentry?, fs[ri[inodekey(key.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), key ∈ ri, inodekey(m) ∈ ri, inodekey(key.ino) ∈ ri, dentrykey(m, str) ∈ ri, asynced → boolvar, ∀ str0. ¬ dentrykey(key.ino, str0) ∈ ri ∧ abs-children(key.ino, fs, ri)[str0] = (∅)[str0], links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ # dentrykeys(inodekey(key.ino), ri) = 0, key.ino = ROOT_INO, dentrykeys(inodekey(key.ino), ri) = ∅, dentrykey(key.ino, str) ∈ ri

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: key name: elim-03 seq: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)) subst: [key, m, str] → [key, m0, str1]

Additional information

Used simplifier rules: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)); (elim) Used terms: key, m0, str1