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Proof step 512 from proof refine-unlink (previous step)

m5 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), dirs = abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- str)] [p_ino, abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- str)][p_ino] .size:= (abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- str)][p_ino].size - 1) ], files = abs-files(fs, ri), ino = mkdentry(str, m0).ino, p_ino = m, mkdentry(str, m0).dentry?, 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, ri[inodekey(m)] ∈ fs, inodekey(m0) ∈ ri, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ m3, abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- str)][p_ino].size ≥ 1, asynced → boolvar0, m5 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m, str), ∀ adr0, adr1, adr2. adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, m1 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(ino; dirs, files); dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m1, m2, m3); dirs, files); afs_inode_sync#(mkinode(m0, md0, false, m5 + 1, 0, m6); 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 := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m1, m2, m3) = p_inode ∧ mkinode(m0, md0, false, m5 + 1, 0, m6) = c_inode ∧ mkdentry(str, m0) = dent ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), m = 0, m0 = ROOT_INO, m0 = 0, m3 = 0, fs[ri[inodekey(m0)]].directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 513:
m5 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), dirs = abs-dirs(fs, ri)[m, mkdir(m3 - 1, md1, m1, m2, abs-children(m, fs, ri) -- str)], files = abs-files(fs, ri), m ≠ 0, m0 ≠ ROOT_INO, m0 ≠ 0, m3 ≠ 0, 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, ri[inodekey(m)] ∈ fs, inodekey(m0) ∈ ri, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ m3, ¬ fs[ri[inodekey(m0)]].directory, asynced → boolvar0, m5 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m, str), ∀ adr0, adr1, adr2. adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, m1 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), ⟨afs_drop_nlink#(mkdentry(str, m0).ino; dirs, files); dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m1, m2, m3); dirs, files); afs_inode_sync#(mkinode(m0, md0, false, m5 + 1, 0, m6); 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 := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m1, m2, m3) = p_inode ∧ mkinode(m0, md0, false, m5 + 1, 0, m6) = c_inode ∧ mkdentry(str, m0) = dent ∧ ENOSPC = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (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)% ⊦ 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)% ⊦ 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)