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Proof step 710 from proof refine-rename-overwrite-reparent-dir (previous step)

1 = fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[inodekey(m)]] = inodenode(key, md6, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, dirs = abs-dirs(fs0, ri0), err = err0, files = abs-files(fs0, ri0), links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), new_child_inode = new_dent_inode, new_dent = old_dent1, new_dent_inode = mkinode(m0, md0, true, 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size), new_inode = mkinode(m7, md1, true, m1, m2, m3), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent0, old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), old_inode = mkinode(m11, md2, true, m4, m16 + 1, m13 + 1), old_parent_inode = old_inode, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, 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(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]), orphans-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m11) ∈ ri0, inodekey(m7) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m7, str0) ∈ ri0, boolvar2 → boolvar0, m4 ≠ 0 ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m0 = ROOT_INO, m0 = 0, m11 = m7, m11 = 0, m7 = 0, pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], adr2 ∈ ri0 -- dentrykey(m11, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], m1 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m11 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 711:
1 = fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m)]] = inodenode(key, md6, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m7, str0) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(m11) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, boolvar2 → boolvar0, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, adr5 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m11, str), adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], m4 = 0 ∧ m11 ≠ ROOT_INO, m1 = 0 ∧ m7 ≠ ROOT_INO, str0 ∈ abs-dirs(fs0, ri0)[m7].entries ∧ m0 = abs-dirs(fs0, ri0)[m7].entries[str0] ∧ str ∈ abs-dirs(fs0, ri0)[m11].entries ∧ m = abs-dirs(fs0, ri0)[m11].entries[str] ∧ m4 = abs-dirs(fs0, ri0)[m11].nlink ∧ m13 + 1 = abs-dirs(fs0, ri0)[m11].size ∧ m16 + 1 = abs-dirs(fs0, ri0)[m11].nsubdirs ∧ m1 = abs-dirs(fs0, ri0)[m7].nlink ∧ m3 = abs-dirs(fs0, ri0)[m7].size ∧ m2 = 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)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (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)% ⊦ 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)