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Proof step 317 from proof refine-unlink (previous step)

m5 + 1 = fs0[ri0[inodekey(m1)]].nlink, 0 = fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m2, m3, m0 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m1), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), old_dent = mkdentry(str, m1), p_inode0 = mkinode(m, md, true, m2, m3, m0 + 1), p_inode1 = mkinode(m1, md0, false, m5 + 1, 0, m6), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(dirs, files), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), pre-unlink(p_inode0, p_inode1, old_dent, dirs, files), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), 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, str))[inodekey(m1), adr3]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced → boolvar0, m2 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) ∧ orphans (abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3])) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m2, m3, m0) = p_inode0 ∧ mkinode(m1, md0, false, m5, 0, m6) = p_inode1 ∧ negdentry(str) = old_dent ∧ ESUCCESS = err0), adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m1 = 0, m1 = ROOT_INO, m5 = 0, fs0[ri0[inodekey(m1)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 318:
m5 + 1 = fs0[ri0[inodekey(m1)]].nlink, 0 = fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m2, m3, m0 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m1), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), old_dent = mkdentry(str, m1), p_inode0 = mkinode(m, md, true, m2, m3, m0 + 1), p_inode1 = mkinode(m1, md0, false, m5 + 1, 0, m6), adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, m1 ≠ 0, m1 ≠ ROOT_INO, m5 ≠ 0, 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, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), 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, str))[inodekey(m1), adr3]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ¬ fs0[ri0[inodekey(m1)]].directory, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, m2 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m2, m3, m0) = p_inode0 ∧ mkinode(m1, md0, false, m5, 0, m6) = p_inode1 ∧ negdentry(str) = old_dent ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ dentrynode(key, m).ino = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)%⊦ abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)) ↔ orphans(fs0, ri0) = orphans(fs, ri); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)% ⊦ mkdir(m, md, m0, m1, entries).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)% ⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)% ⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-unlink(p_inode, c_inode, dent, dirs, files) ↔ valid-dentry(p_inode.ino, dent, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ valid-dir-inode(p_inode, dirs, files) ∧ c_inode.ino = dent.ino; (s)