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Proof step 116 from proof refine-rmdir (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, abs-children(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅, adr = adr3, dentrykeys(inodekey(fs0[ri0[dentrykey(m, str)]].ino), ri0) = ∅, fs = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], fs1 = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], key = inodekey(fs0[ri0[dentrykey(m, str)]].ino), key0 = dentrykey(m, mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name), links(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri1 -- key0, ri1 = ri0[inodekey(m), adr1], ro = orphans(fs0, ri0), ro1 = orphans(fs0, ri0), fs0[ri0[dentrykey(m, str)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, 1 ≤ fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].nsubdirs ≥ 1, fs0[ri0[inodekey(m)]].size ≥ 1, asynced → boolvar0, fs0[ri0[inodekey(m)]].trunc? ∨ fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].trunc? ∨ fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].inode?, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ [if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; ro0 := orphans(fs0, ri0); aubifs_core_orphans_insert# (inodekey(fs0[ri0[dentrykey(m, str)]].ino), ri, fi, fo, fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ro0); dent := negdentry(mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name); p_inode := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1).size); c_inode := mkinode (fs0[ri0[dentrykey(m, str)]].ino, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) .meta, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) .directory, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) .nlink, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) .nsubdirs, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) .size)] ( ubifs-cons (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri, ro0, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri, ro0, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri) ∧ orphans-cons (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri, ro0) ∧ ri-inj(ri) ∧ log-cons (log0, fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ]) ∧ ro0.inodes? → ⟨old_dent := mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino); p_inode0 := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); p_inode1 := mkinode (fs0[ri0[dentrykey(m, str)]].ino, md0, true, 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_rmdir#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri) ∧ files = abs-files (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri) ∧ orphans (abs-dirs (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri), abs-files (fs0 [adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs - 1, fs0[ri0[inodekey(m)]].size - 1) ] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ ESUCCESS = err0)), fs0[ri0[dentrykey(m, str)]].ino = 0, fs0[ri0[dentrykey(m, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m)]].nsubdirs = 0, fs0[ri0[inodekey(m)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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