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Proof step 276 from proof refine-link (previous step)

fs[ri[dentrykey(ino0, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, fs[ri[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, 0 = fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nsubdirs, mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = mkinode(m0, md1, boolvar1, m1, m2, m3), fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(ino0)]].directory, 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(ino2) ∈ ri, dentrykey(ino2, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, inodekey(ino1) ∈ ri, inodekey(fs[ri[dentrykey(ino2, str)]].ino) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(m) ∈ ri, inodekey(ino0) ∈ ri, dentrykey(ino0, str) ∈ ri, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, links(ino2, abs-dirs(fs, ri)) ≠ ∅ ∨ ino2 = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink ≠ 0 ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(fs[ri[dentrykey(ino2, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), ⟨let p_ino = m0 in {dirs := abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= abs-dirs(fs, ri)[p_ino].entries[str0, mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino] ]; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino in {files := abs-files(fs, ri); afs_inc_nlink#(ino; dirs, files)}; new_dent := mkdentry(str0, mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino); afs_inode_sync#(mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size); dirs, files); afs_inode_sync# (mkinode(fs[ri[dentrykey(ino0, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, 0, m6); dirs, files); p_inode := getinode(m0, dirs, files); c_inode := getinode(mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino, dirs, files); err := ESUCCESS}; 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_inode ∧ mkinode(fs[ri[dentrykey(ino0, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, 0, m6) = c_inode ∧ negdentry(str0) = new_dent ∧ ENOSPC = err), fs[ri[dentrykey(ino2, str)]].ino = 0, m = 0, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].directory, dentrykey(m, str0) ∈ ri, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink = 0 ∧ fs[ri[dentrykey(ino2, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 277:
fs[ri[dentrykey(ino0, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, fs[ri[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, 0 = fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nsubdirs, fs[ri[dentrykey(ino2, str)]].ino ≠ 0, m0 ≠ 0, fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(ino0)]].directory, 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(ino2) ∈ ri, dentrykey(ino2, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, inodekey(ino1) ∈ ri, inodekey(fs[ri[dentrykey(ino2, str)]].ino) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(m0) ∈ ri, inodekey(ino0) ∈ ri, dentrykey(ino0, str) ∈ ri, ¬ fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].directory, ¬ dentrykey(m0, str0) ∈ ri, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, links(ino2, abs-dirs(fs, ri)) ≠ ∅ ∨ ino2 = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink ≠ 0 ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m0, abs-dirs(fs, ri)) ≠ ∅ ∨ m0 = ROOT_INO, links(fs[ri[dentrykey(ino2, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO ⊦ ⟨let p_ino = m0 in {dirs := abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= abs-dirs(fs, ri)[p_ino].entries[str0, mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino] ]; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino in {files := abs-files(fs, ri); afs_inc_nlink#(ino; dirs, files)}; new_dent := mkdentry(str0, mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino); afs_inode_sync#(mkinode(m0, md, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size); dirs, files); afs_inode_sync# (mkinode(fs[ri[dentrykey(ino0, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, 0, m6); dirs, files); p_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) ); c_inode := getinode(mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino).ino, dirs, files); err := ESUCCESS}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m0, md, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = p_inode ∧ mkinode(fs[ri[dentrykey(ino0, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, 0, m6) = c_inode ∧ negdentry(str0) = new_dent ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink = 0 ∧ fs[ri[dentrykey(ino2, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)