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Proof step 397 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name)] [p_ino, abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size:= ( abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size - 1) ] [p_ino, abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino, abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size:= ( abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size - 1) ] [p_ino ] .nsubdirs:= ( abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino, abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size:= ( abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino] .entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size - 1) ] [p_ino ] .nsubdirs - 1) ], files = abs-files(fs, ri), ino = mkdentry(str, fs[ri[dentrykey(m, str)]].ino).ino, links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), p_ino = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size).ino, mkdentry(str, fs[ri[dentrykey(m, str)]].ino).dentry?, fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m)]].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), ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, 1 ≤ fs[ri[inodekey(m)]].size, abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name)] [p_ino, abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size:= ( abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name) ] [p_ino ] .size - 1) ] [p_ino ] .nsubdirs ≥ 1, abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name)] [p_ino ] .size ≥ 1, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, fs[ri[inodekey(m)]].trunc? ∨ fs[ri[inodekey(m)]].inode?, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(ino; dirs, files); dent := negdentry(mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name); afs_inode_sync#(mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size); dirs, files); afs_inode_sync# (mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size) ; dirs, files); p_inode := getinode(mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size).ino, dirs, files); c_inode := getinode (mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size) .ino, dirs, files); err := ESUCCESS; 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_inode ∧ mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size) = c_inode ∧ mkdentry(str, fs[ri[dentrykey(m, str)]].ino) = dent ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), fs[ri[dentrykey(m, str)]].ino = 0, fs[ri[dentrykey(m, str)]].ino = ROOT_INO, fs[ri[inodekey(m)]].nsubdirs = 0, fs[ri[inodekey(m)]].size = 0, m = 0, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 398:
1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri) [m, mkdir (fs[ri[inodekey(m)]].size - 1, fs[ri[inodekey(m)]].meta, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs - 1, abs-children(m, fs, ri) -- str) ], files = abs-files(fs, ri), links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), fs[ri[dentrykey(m, str)]].ino ≠ ROOT_INO, fs[ri[dentrykey(m, str)]].ino ≠ 0, fs[ri[inodekey(m)]].nsubdirs ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, m ≠ 0, fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, 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, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, 1 ≤ fs[ri[inodekey(m)]].size, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, fs[ri[dentrykey(m, str)]].ino).ino; dirs, files); dent := negdentry(mkdentry(str, fs[ri[dentrykey(m, str)]].ino).name); afs_inode_sync#(mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size); dirs, files); afs_inode_sync# (mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size) ; dirs, files); p_inode := getinode(mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size).ino, dirs, files); c_inode := getinode (mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size) .ino, dirs, files); err := ESUCCESS; 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_inode ∧ mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size) = c_inode ∧ mkdentry(str, fs[ri[dentrykey(m, str)]].ino) = dent ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ mkdir(m, md, m0, m1, entries).nsubdirs:= m4 = mkdir(m, md, m0, m4, entries); (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)