[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 490 from proof refine-unlink (previous step)

m5 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, 0 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, adr4 = adr1, c_inode = mkinode(m3, md0, false, m5 + 1, 0, m6), dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), dirs = abs-dirs(fs, ri), err = ENOSPC, files = abs-files(fs, ri), m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, m3 = fs[ri[dentrykey(m, str)]].ino, m4 = m5 + 1, nd = inodenode(inodekey(m3), md0, false, m5, 0, m6), nd0 = dentrynode(dentrykey(m, dent.name), 0), nd1 = inodenode(inodekey(m), md, true, m0, m1, m2 - 1), p_inode = mkinode(m, md, true, m0, m1, m2), ro = orphans(fs, ri), ro0 = orphans(fs, ri), fs[ri[inodekey(m)]].directory, 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), node-cons(nd1.key, nd1), node-cons(nd0.key, nd0), node-cons(nd.key, nd), 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, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, m2 ≥ 1, asynced → boolvar0, m5 = 0 → links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), ∀ adr1, adr2, adr3. ¬(new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ')), fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ [if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m), adr4, fi, ro0, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m, dent.name), fi, ro0, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m3), adr, fi, ro0, fo, fs, log, boolvar; ri); if m4 = 1 then aubifs_core_orphans_insert#(inodekey(m3), ri, fi, fo, fs, log, boolvar; ro0); dent := negdentry(dent.name); p_inode := mkinode (p_inode.ino, inodenode(inodekey(m), md, true, m0, m1, m2 - 1).meta, inodenode(inodekey(m), md, true, m0, m1, m2 - 1).directory, inodenode(inodekey(m), md, true, m0, m1, m2 - 1).nlink, inodenode(inodekey(m), md, true, m0, m1, m2 - 1).nsubdirs, inodenode(inodekey(m), md, true, m0, m1, m2 - 1).size); c_inode := mkinode (m3, inodenode(inodekey(m3), md0, false, m5, 0, m6).meta, inodenode(inodekey(m3), md0, false, m5, 0, m6).directory, inodenode(inodekey(m3), md0, false, m5, 0, m6).nlink, inodenode(inodekey(m3), md0, false, m5, 0, m6).nsubdirs, inodenode(inodekey(m3), md0, false, m5, 0, m6).size)}] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro0.inodes? → ⟨old_dent := mkdentry(str, m3); p_inode0 := mkinode(m, md, true, m0, m1, m2); p_inode1 := mkinode(m3, md0, false, m4, 0, m6); afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), fs[ri[dentrykey(m, str)]].ino = ROOT_INO, fs[ri[inodekey(m)]].size = 0, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 491:
m5 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, 0 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[dentrykey(m, str)]].ino ≠ 0, fs[ri[dentrykey(m, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m)]].size ≠ 0, m ≠ 0, fs[ri[inodekey(m)]].directory, 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, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, asynced → boolvar0, m5 = 0 → links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), ∀ adr0, adr1, adr2. adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ [skip] ⟨old_dent := mkdentry(str, fs[ri[dentrykey(m, str)]].ino); p_inode0 := mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size); p_inode1 := mkinode(fs[ri[dentrykey(m, str)]].ino, md0, false, m5 + 1, 0, m6); dirs := abs-dirs(fs, ri); files := abs-files(fs, ri); afs_unlink#(; p_inode0, p_inode1, old_dent, err0, 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(fs[ri[dentrykey(m, str)]].ino, md0, false, m5 + 1, 0, m6) = p_inode1 ∧ mkdentry(str, fs[ri[dentrykey(m, str)]].ino) = old_dent ∧ ENOSPC = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)% ⊦ ESUCCESS ≠ ENOSPC; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)