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Proof step 468 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(m0)]].nlink, fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), links(m0, fs, ri) = ∅ ++ dentrykey(m, str), old_dent = mkdentry(str, m0), p_inode0 = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(m0)]].inode?, fs[ri[inodekey(m)]].inode?, 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-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, ri[dentrykey(m, str)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ⌊err0⌋ , asynced → boolvar0, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode0, p_inode1, old_dent, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = p_inode0 ∧ mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = p_inode1 ∧ mkdentry(str, m0) = old_dent ∧ err0 = err1), fs[ri[inodekey(m)]].nsubdirs = 0, fs[ri[inodekey(m)]].size = 0, m = 0, m0 = 0, m0 = ROOT_INO, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 469:
1 = fs[ri[inodekey(m0)]].nlink, fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), links(m0, fs, ri) = ∅ ++ dentrykey(m, str), old_dent = mkdentry(str, m0), p_inode0 = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), fs[ri[inodekey(m)]].nsubdirs ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, m ≠ 0, m0 ≠ ROOT_INO, m0 ≠ 0, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m)]].inode?, fs[ri[inodekey(m0)]].inode?, 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-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, 1 ≤ fs[ri[inodekey(m)]].size, ⌊err0⌋ , asynced → boolvar0, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode0, p_inode1, old_dent, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = p_inode0 ∧ mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = p_inode1 ∧ mkdentry(str, m0) = old_dent ∧ err0 = err1), fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)% ⊦ dentrynode(key, m).dentry?; (s)%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]