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Proof step 416 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(m)]].nlink, fs[ri[dentrykey(m2, str)]] = dentrynode(key, m), fs[ri[inodekey(m2)]] = inodenode(key0, md1, true, m3, m1 + 1, m0 + 1), abs-children(m, fs, ri) = ∅, dentrykeys(inodekey(m), ri) = ∅, dirs = dirs0[ino, dirs0[ino].nlink:= (dirs0[ino].nlink - 1)], dirs0 = abs-dirs(fs, ri)[m2, mkdir(m0, md1, m3, m1, abs-children(m2, fs, ri) -- str)], files = abs-files(fs, ri), ino = mkdentry(str, m).ino, links(m, fs, ri) = ∅ ++ dentrykey(m2, str), mkdentry(str, m).dentry?, 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), ri[inodekey(m2)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m2, str)] ∈ fs, dentrykey(m2, str) ∈ ri, inodekey(m2) ∈ ri, dirs0[ino].nlink ≥ 1, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, links(m2, abs-dirs(fs, ri)) ≠ ∅ ∨ m2 = ROOT_INO, m3 ≠ 0 ∨ m2 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m2, md, true, m3, m1 + 1, m0 + 1); dirs, files); afs_inode_sync#(mkinode(m, md0, true, 1, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size); dirs, files); p_inode := (m2 ∈ dirs ⊃ mkinode(m2, dirs[m2].meta, true, dirs[m2].nlink, dirs[m2].nsubdirs, dirs[m2].size) ;mkinode(m2, files[m2].meta, false, files[m2].nlink, 0, files[m2].size) ); c_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) ); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m2, md, true, m3, m1 + 1, m0 + 1) = p_inode ∧ mkinode(m, md0, true, 1, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = c_inode ∧ mkdentry(str, m) = negdentry(str) ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), m = ROOT_INO, m = 0, m2 = 0, m3 = 0 ∧ m2 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 417:
1 = fs[ri[inodekey(m)]].nlink, fs[ri[dentrykey(m2, str)]] = dentrynode(key, m), fs[ri[inodekey(m2)]] = inodenode(key0, md1, true, m3, m1 + 1, m0 + 1), abs-children(m, fs, ri) = ∅, dentrykeys(inodekey(m), ri) = ∅, links(m, fs, ri) = ∅ ++ dentrykey(m2, str), (m = m2 ⊃ mkdir(m0, md1, m3, m1, abs-children(m2, fs, ri) -- str) ;mkdir(fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].meta, 1, fs[ri[inodekey(m)]].nsubdirs, ∅) ) .nlink ≠ 0, m ≠ ROOT_INO, m ≠ 0, m2 ≠ 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), ri[inodekey(m2)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m2, str)] ∈ fs, dentrykey(m2, str) ∈ ri, inodekey(m2) ∈ ri, 1 ≤ (m = m2 ⊃ mkdir(m0, md1, m3, m1, abs-children(m2, fs, ri) -- str) ;mkdir(fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].meta, 1, fs[ri[inodekey(m)]].nsubdirs, ∅) ) .nlink, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, links(m2, abs-dirs(fs, ri)) ≠ ∅ ∨ m2 = ROOT_INO, m3 ≠ 0 ∨ m2 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), m3 = 0 ∧ m2 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (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)% ⊦ mkdentry(str, m).ino = m; (s)