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Proof step 163 from proof refine-rmdir (previous step)

1 = fs0[ri0[inodekey(m4)]].nlink, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m4), fs0[ri0[inodekey(m4)]] = inodenode(key1, md2, true, 1, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size), abs-children(m4, fs0, ri0) = ∅, dentrykeys(inodekey(m4), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m, mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)], files = abs-files(fs0, ri0), links(m4, fs0, ri0) = ∅ ++ dentrykey(m, str), adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, m4 ≠ 0, m4 ≠ ROOT_INO, fs0[ri0[inodekey(m4)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m4) ∈ ri0, ri0[inodekey(m4)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, m3 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, m4).ino; dirs, files); dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m3, m0 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m4, md0, true, 1, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (m4 ∈ dirs ⊃ mkinode(m4, dirs[m4].meta, true, dirs[m4].nlink, dirs[m4].nsubdirs, dirs[m4].size) ;mkinode(m4, files[m4].meta, false, files[m4].nlink, 0, files[m4].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) = orphans(fs0, ri0) ++ inodekey(m4) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m3, m0, m1) = p_inode ∧ mkinode(m4, md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) = c_inode ∧ negdentry(str) = dent ∧ ESUCCESS = err), m3 = 0 ∧ m ≠ ROOT_INO

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 164:
1 = fs0[ri0[inodekey(m4)]].nlink, fs0[ri0[inodekey(m4)]] = inodenode(key1, md2, true, 1, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m4), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), abs-children(m4, fs0, ri0) = ∅, dentrykeys(inodekey(m4), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m, mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)], files = abs-files(fs0, ri0), ino = mkdentry(str, m4).ino, links(m4, fs0, ri0) = ∅ ++ dentrykey(m, str), mkdentry(str, m4).dentry?, fs0[ri0[inodekey(m4)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m4)] ∈ fs0, inodekey(m4) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, m3 ≠ 0 ∨ m = ROOT_INO ⊦ ⟨if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m3, m0 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m4, md0, true, 1, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (m4 ∈ dirs ⊃ mkinode(m4, dirs[m4].meta, true, dirs[m4].nlink, dirs[m4].nsubdirs, dirs[m4].size) ;mkinode(m4, files[m4].meta, false, files[m4].nlink, 0, files[m4].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) = orphans(fs0, ri0) ++ inodekey(m4) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m3, m0, m1) = p_inode ∧ mkinode(m4, md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) = c_inode ∧ negdentry(str) = dent ∧ ESUCCESS = err), adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m4 = 0, m4 = ROOT_INO, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, m3 = 0 ∧ m ≠ ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_drop_nlink#(INO; DIRS, FILES) {if INO ∈ DIRS then DIRS[INO].nlink := DIRS[INO].nlink - 1; if INO ∈ FILES then FILES[INO].nlink := FILES[INO].nlink - 1 };% ⊦ mkdentry(str, m).dentry?; (s)