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Proof step 53 from proof refine-rmdir (previous step)

abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri)[str] = (∅)[str], 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, ∀ 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, dentrykey(fs[ri[dentrykey(m, str)]].ino, str) ∈ ri, ∀ key. key ∈ dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) ↔ key ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
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

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ks ≠ ∅ → # ks ≠ 0; (forward) from specification set-basic[node-index]%size-zero: ⊦ # ks ≠ 0 → ks ≠ ∅; (forward) from specification set-basic[node-index]% ⊦ ¬ key ∈ ∅; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ dentrykeys(key0, ri) ↔ key ∈ ri ∧ key.dentry? ∧ key0.inode? ∧ key.ino = key0.ino; (s)