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Proof step 406 from proof refine-rmdir (previous step)

fs[ri[inodekey(m2)]].nsubdirs = m1 + 1, fs[ri[inodekey(m2)]].size = m0 + 1, 1 = fs[ri[inodekey(fs[ri[dentrykey(m2, str)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m2, str)]].ino, fs, ri) = ∅, dentrykeys(inodekey(fs[ri[dentrykey(m2, str)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri)[m2, mkdir(m0, fs[ri[inodekey(m2)]].meta, fs[ri[inodekey(m2)]].nlink, m1, abs-children(m2, fs, ri) -- str)], files = abs-files(fs, ri), links(fs[ri[dentrykey(m2, str)]].ino, fs, ri) = ∅ ++ dentrykey(m2, str), fs[ri[dentrykey(m2, str)]].ino ≠ ROOT_INO, fs[ri[dentrykey(m2, str)]].ino ≠ 0, m2 ≠ 0, fs[ri[dentrykey(m2, str)]].dentry?, fs[ri[inodekey(m2)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m2, str)]].ino)]].directory, fs[ri[inodekey(m2)]].inode?, fo.inodes?, orphans(fs, ri).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(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m2) ∈ ri, dentrykey(m2, str) ∈ ri, ri[dentrykey(m2, str)] ∈ fs, inodekey(fs[ri[dentrykey(m2, str)]].ino) ∈ ri, ri[inodekey(m2)] ∈ fs, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, fs[ri[inodekey(m2)]].nlink ≠ 0 ∨ m2 = ROOT_INO, links(m2, abs-dirs(fs, ri)) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, fs[ri[dentrykey(m2, str)]].ino).ino; dirs, files); dent := negdentry(mkdentry(str, fs[ri[dentrykey(m2, str)]].ino).name); afs_inode_sync#(mkinode(m2, md, true, fs[ri[inodekey(m2)]].nlink, fs[ri[inodekey(m2)]].nsubdirs, fs[ri[inodekey(m2)]].size); dirs, files); afs_inode_sync# (mkinode (fs[ri[dentrykey(m2, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m2, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m2, str)]].ino)]].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 := (fs[ri[dentrykey(m2, str)]].ino ∈ dirs ⊃ mkinode (fs[ri[dentrykey(m2, str)]].ino, dirs[fs[ri[dentrykey(m2, str)]].ino].meta, true, dirs[fs[ri[dentrykey(m2, str)]].ino].nlink, dirs[fs[ri[dentrykey(m2, str)]].ino].nsubdirs, dirs[fs[ri[dentrykey(m2, str)]].ino].size) ;mkinode (fs[ri[dentrykey(m2, str)]].ino, files[fs[ri[dentrykey(m2, str)]].ino].meta, false, files[fs[ri[dentrykey(m2, str)]].ino].nlink, 0, files[fs[ri[dentrykey(m2, str)]].ino].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m2, md, true, fs[ri[inodekey(m2)]].nlink, fs[ri[inodekey(m2)]].nsubdirs, fs[ri[inodekey(m2)]].size) = p_inode ∧ mkinode (fs[ri[dentrykey(m2, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m2, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m2, str)]].ino)]].size) = c_inode ∧ mkdentry(str, fs[ri[dentrykey(m2, str)]].ino) = dent ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), fs[ri[inodekey(m2)]].nlink = 0 ∧ m2 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 407:
fs[ri[inodekey(m2)]].nsubdirs = m1 + 1, fs[ri[inodekey(m2)]].size = m0 + 1, 1 = fs[ri[inodekey(m)]].nlink, fs[ri[dentrykey(m2, str)]] = dentrynode(key, m), abs-children(m, fs, ri) = ∅, dentrykeys(inodekey(m), ri) = ∅, dirs = abs-dirs(fs, ri)[m2, mkdir(m0, fs[ri[inodekey(m2)]].meta, fs[ri[inodekey(m2)]].nlink, m1, abs-children(m2, fs, ri) -- str)], files = abs-files(fs, ri), links(m, fs, ri) = ∅ ++ dentrykey(m2, str), fs[ri[dentrykey(m2, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m2)]].directory, fs[ri[inodekey(m2)]].inode?, 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, 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, fs[ri[inodekey(m2)]].nlink ≠ 0 ∨ m2 = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, m).ino; dirs, files); dent := negdentry(mkdentry(str, m).name); afs_inode_sync#(mkinode(m2, md, true, fs[ri[inodekey(m2)]].nlink, fs[ri[inodekey(m2)]].nsubdirs, fs[ri[inodekey(m2)]].size); 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, fs[ri[inodekey(m2)]].nlink, fs[ri[inodekey(m2)]].nsubdirs, fs[ri[inodekey(m2)]].size) = p_inode ∧ mkinode(m, md0, true, 1, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = c_inode ∧ mkdentry(str, m) = dent ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), m = ROOT_INO, m = 0, m2 = 0, fs[ri[inodekey(m2)]].nlink = 0 ∧ m2 ≠ ROOT_INO

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs[ri[dentrykey(m2, str)]], key, m]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(m2, str)]], key, m