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Proof step 89 from proof refine-link (previous step)

fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino, str)]].ino, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), old_dent0 = negdentry(str0), p_inode0 = mkinode(m, md, true, m0, m1, m2), p_inode1 = mkinode(fs0[ri0[dentrykey(ino, str)]].ino, md0, false, m3, 0, m6), fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino0)]].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(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]), 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(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, 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(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)), 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(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), 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(ino, 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(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), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(ino0, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)] ∈ fs0, dentrykey(ino, str) ∈ ri0, dentrykey(ino1, str) ∈ ri0, inodekey(ino) ∈ ri0, inodekey(ino1) ∈ ri0, inodekey(ino0) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced → boolvar0, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino, 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(ino0, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino, str)]].ino = ROOT_INO ⊦ fs0[ri0[dentrykey(ino, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, m3 = 0 ∧ fs0[ri0[dentrykey(ino, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, afs-cons(dirs, files) ∧ pre-link(p_inode0, p_inode1, mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino), old_dent0, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 90:
fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino, str)]].ino, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino0)]].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(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]), 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(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, 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(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)), 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(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), 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(ino, 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(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), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(ino0, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)] ∈ fs0, dentrykey(ino, str) ∈ ri0, dentrykey(ino1, str) ∈ ri0, inodekey(ino) ∈ ri0, inodekey(ino1) ∈ ri0, inodekey(ino0) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced → boolvar0, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino, 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(ino0, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino, str)]].ino = ROOT_INO ⊦ fs0[ri0[dentrykey(ino, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ∃ ino2. inodekey(ino2) ∈ ri0 ∧ (links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO) ∧ dentrykey(ino2, str) ∈ ri0 ∧ fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, m3 = 0 ∧ fs0[ri0[dentrykey(ino, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ negdentry(str).negdentry?; (s)% ⊦ negdentry(str).name = str; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (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)% ⊦ mkdentry(str, m).name = str; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)%⊦ valid-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, files)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)