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Proof step 103 from proof refine-rename-overwrite-keep-parent-different (previous step)

¬ fs0[ri0[inodekey(m3)]].directory ↔ ¬ fs0[ri0[inodekey(m)]].directory, fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), links(m3, fs0, ri0) = ∅ ++ dentrykey(m7, str0), new_dent_inode = mkinode(m3, md0, boolvar2, 1, m5, m6), new_inode = mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m3), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_inode = mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m7, str)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m7) ∈ ri0, dentrykey(m7, str0) ∈ ri0, dentrykey(m7, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m) ∈ ri0, fs0[ri0[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri0) = ∅, fs0[ri0[inodekey(m3)]].directory → abs-children(m3, fs0, ri0) = ∅, boolvar3 → boolvar4, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m7 = ROOT_INO, fs0[ri0[inodekey(m3)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m6 = fs0[ri0[inodekey(m3)]].size ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∨ fs0[ri0[inodekey(m3)]].directory ∧ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ m6 = fs0[ri0[inodekey(m3)]].size ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m3 = 0, m3 = ROOT_INO, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m7, str), adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], m4 = 0 ∧ m7 ≠ ROOT_INO, afs-cons(dirs, files) ∧ pre-rename(old_inode, old_dent0, old_dent_inode, new_inode, old_dent1, new_dent_inode, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 104:
¬ fs0[ri0[inodekey(m3)]].directory ↔ ¬ fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), links(m3, fs0, ri0) = ∅ ++ dentrykey(m7, str0), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), inodekey(m) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m7, str) ∈ ri0, dentrykey(m7, str0) ∈ ri0, inodekey(m7) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str)] ∈ fs0, boolvar3 → boolvar4, fs0[ri0[inodekey(m3)]].directory → abs-children(m3, fs0, ri0) = ∅, fs0[ri0[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri0) = ∅, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∨ fs0[ri0[inodekey(m3)]].directory ∧ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ m6 = fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m6 = fs0[ri0[inodekey(m3)]].size ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2, m4 ≠ 0 ∨ m7 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m3 = ROOT_INO, m3 = 0, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], adr2 ∈ ri0 -- dentrykey(m7, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], m4 = 0 ∧ m7 ≠ ROOT_INO, str0 ∈ abs-dirs(fs0, ri0)[m7].entries ∧ m3 = abs-dirs(fs0, ri0)[m7].entries[str0] ∧ ( fs0[ri0[inodekey(abs-dirs(fs0, ri0)[m7].entries[str0])]].directory ∧ 1 = fs0[ri0[inodekey(abs-dirs(fs0, ri0)[m7].entries[str0])]].nlink ∧ m6 = fs0[ri0[inodekey(abs-dirs(fs0, ri0)[m7].entries[str0])]].size ∧ m5 = fs0[ri0[inodekey(abs-dirs(fs0, ri0)[m7].entries[str0])]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(abs-dirs(fs0, ri0)[m7].entries[str0])]].directory ∧ 1 = fs0[ri0[inodekey(abs-dirs(fs0, ri0)[m7].entries[str0])]].nlink ∧ m5 = 0 ∧ ¬ boolvar2) ∧ str ∈ abs-dirs(fs0, ri0)[m7].entries ∧ m = abs-dirs(fs0, ri0)[m7].entries[str] ∧ m4 = abs-dirs(fs0, ri0)[m7].nlink ∧ m11 + 1 = abs-dirs(fs0, ri0)[m7].size ∧ n0 + (boolvar1 ⊃ 1;0) = abs-dirs(fs0, ri0)[m7].nsubdirs

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (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)%⊦ 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)% ⊦ 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)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ mkdentry(str, m).dentry?; (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)%⊦ 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)% ⊦ ¬ mkdentry(str, m).negdentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ 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-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)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)