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Proof step 49 from proof refine-rmdir (previous step)

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. (str0 ∈ abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) ↔ str0 ∈ ∅) ∧ 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) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
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, dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ ∅; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)