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Proof step 103 from proof refine-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[dentrykey(ino3, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino4, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino2, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), dirs = abs-dirs(fs0, ri0)[m, mkdir(m2 + 1, md1, m0, m1, abs-children(m, fs0, ri0)[str0, fs0[ri0[dentrykey(ino2, str)]].ino])], files = abs-files(fs0, ri0), fs0[ri0[dentrykey(ino2, str)]].ino ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m ≠ 0, fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino3)]].directory, fs0[ri0[inodekey(ino4)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino2)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(ino4) ∈ ri0, dentrykey(ino3, str) ∈ ri0, inodekey(ino3) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ino1) ∈ ri0, inodekey(ino) ∈ ri0, dentrykey(ino1, str) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino2, str)]].ino) ∈ ri0, ri0[dentrykey(ino4, str)] ∈ fs0, dentrykey(ino4, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino2, str) ∈ ri0, ri0[dentrykey(ino, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ dentrykey(m, str0) ∈ ri0, asynced → boolvar0, links(ino3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino3 = ROOT_INO, links(fs0[ri0[dentrykey(ino2, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(ino4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino4 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ ⟨afs_inc_nlink#(mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino).ino); afs_inode_sync#(mkinode(m, md, true, m0, m1, m2); dirs, files); afs_inode_sync#(mkinode(fs0[ri0[dentrykey(ino2, str)]].ino, md0, false, m3, 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 := getinode(mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode ∧ mkinode(fs0[ri0[dentrykey(ino, str)]].ino, md0, false, m3 + 1, 0, m6) = c_inode ∧ mkdentry(str0, fs0[ri0[dentrykey(ino, str)]].ino) = new_dent ∧ ESUCCESS = err), fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, m3 = 0 ∧ fs0[ri0[dentrykey(ino2, str)]].ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 104:
fs0[ri0[dentrykey(ino3, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino4, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino2, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino, str)]] = dentrynode(key2, m4), dirs = abs-dirs(fs0, ri0)[m, mkdir(m2 + 1, md1, m0, m1, abs-children(m, fs0, ri0)[str0, fs0[ri0[dentrykey(ino2, str)]].ino])], files = abs-files(fs0, ri0), m4 = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino2)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino4)]].directory, fs0[ri0[inodekey(ino3)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino, str)] ∈ fs0, dentrykey(ino2, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino4, str) ∈ ri0, ri0[dentrykey(ino4, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino2, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)] ∈ fs0, dentrykey(ino1, str) ∈ ri0, inodekey(ino) ∈ ri0, inodekey(ino1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino3) ∈ ri0, dentrykey(ino3, str) ∈ ri0, inodekey(ino4) ∈ ri0, asynced → boolvar0, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino4 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino2, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, links(ino3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟨afs_inc_nlink#(mkdentry(str, m4).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, m4).ino); afs_inode_sync#(mkinode(m, md, true, m0, m1, m2); dirs, files); afs_inode_sync#(mkinode(fs0[ri0[dentrykey(ino2, str)]].ino, md0, false, m3, 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 := getinode(mkdentry(str, m4).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), m4)] [adr3, inodenode(inodekey(m4), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(m4), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), m4)] [adr3, inodenode(inodekey(m4), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(m4), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), m4)] [adr3, inodenode(inodekey(m4), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(m4), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode ∧ mkinode(m4, md0, false, m3 + 1, 0, m6) = c_inode ∧ mkdentry(str0, m4) = new_dent ∧ ESUCCESS = err), fs0[ri0[dentrykey(ino2, str)]].ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m, str0) ∈ ri0, m3 = 0 ∧ fs0[ri0[dentrykey(ino2, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ 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] → [fs0[ri0[dentrykey(ino, str)]], key2, m4]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs0[ri0[dentrykey(ino, str)]], key2, m4