Proof step 160 from proof refine-rmdir (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 161:

  1 = fs0[ri0[inodekey(m2)]].nlink, fs0[ri0[inodekey(m2)]] = inodenode(key1, md2, true, 1, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m2), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), abs-children(m2, fs0, ri0) = ∅, dentrykeys(inodekey(m2), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m, mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)], files = abs-files(fs0, ri0), links(m2, fs0, ri0) = ∅ ++ dentrykey(m, str), adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, m2 ≠ 0, m2 ≠ ROOT_INO, fs0[ri0[inodekey(m2)]].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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3], orphans(fs0, ri0) ++ inodekey(m2)), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3], orphans(fs0, ri0) ++ inodekey(m2), 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(m2), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3], orphans(fs0, ri0) ++ inodekey(m2), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m2) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, m3 ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, m2).ino; dirs, files); dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m3, m0 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m2, md0, true, 1, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].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 := getinode(mkinode(m2, md0, true, 1, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size).ino, dirs, files); 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3]) = orphans(fs0, ri0) ++ inodekey(m2) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m3, m0, m1) = p_inode ∧ mkinode(m2, md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) = c_inode ∧ negdentry(str) = dent ∧ ESUCCESS = err), m3 = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ m + 1 ≠ 0; (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)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (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)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (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)%⊦ 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)