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Proof step 317 from proof inv-rename-overwrite-reparent (previous step)

¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[inodekey(m)]] = inodenode(key2, md3, true, m10, n0 + (boolvar3 ⊃ 1;0), m1 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), adr = adr5, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, m6, m7) ], fs1 = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, m6, m7) ], key = inodekey(mkdentry(str0, m8).ino), log = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', log1 = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', nd = inodenode(inodekey(mkdentry(str0, m8).ino), md2, boolvar1, m11, m6, m7), new_dent = mkdentry(str0, m8), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], mkdentry(str0, m8).dentry?, nd.inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m0, str0)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, adr ∈ fs1, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, m11 = 0 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(m8)]].nlink ∧ m6 = fs0[ri0[inodekey(m8)]].nsubdirs ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(m8)]].nlink ∧ m6 = fs0[ri0[inodekey(m8)]].nsubdirs ∧ m7 = fs0[ri0[inodekey(m8)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri0[inodekey(m5)]].size, m9 ≠ 0 ∨ m0 = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO ⊦ ⟪new_dent := mkdentry(new_dent.name, mkdentry(str, m5).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m10, n0, m1).meta, inodenode(inodekey(m), md, true, m10, n0, m1).directory, inodenode(inodekey(m), md, true, m10, n0, m1).nlink, inodenode(inodekey(m), md, true, m10, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m10, n0, m1).size); new_child_inode := mkinode(m8, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), nd.nlink = 0, adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m = 0, m0 = 0, m0 = m, m8 = 0, m8 = ROOT_INO, adr ∈ ri1, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3]

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 318:
¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m)]] = inodenode(key2, md3, true, m10, n0 + (boolvar3 ⊃ 1;0), m1 + 1), adr = adr5, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, m6, m7) ], fs1 = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, m6, m7) ], key = inodekey(mkdentry(str0, m8).ino), log = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', log1 = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', nd = inodenode(inodekey(mkdentry(str0, m8).ino), md2, boolvar1, m11, m6, m7), new_dent = mkdentry(str0, m8), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], mkdentry(str, m5).dentry?, mkdentry(str0, m8).dentry?, nd.inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), adr ∈ fs1, ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, m11 = 0 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri0[inodekey(m5)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(m8)]].nlink ∧ m6 = fs0[ri0[inodekey(m8)]].nsubdirs ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(m8)]].nlink ∧ m6 = fs0[ri0[inodekey(m8)]].nsubdirs ∧ m7 = fs0[ri0[inodekey(m8)]].size ⊦ ⟪old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m10, n0, m1).meta, inodenode(inodekey(m), md, true, m10, n0, m1).directory, inodenode(inodekey(m), md, true, m10, n0, m1).nlink, inodenode(inodekey(m), md, true, m10, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m10, n0, m1).size); new_child_inode := mkinode(m8, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), nd.nlink = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m = 0, m0 = m, m0 = 0, m8 = ROOT_INO, m8 = 0, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], adr ∈ ri1

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ mkdentry(str, m).dentry?; (s)