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Proof step 39 from proof inv-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], key = inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2], fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), 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), ri0[inodekey(m3)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, inodekey(ino) ∈ ri0, inodekey(ino0) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(ino0, str) ∈ ri0, fs0[ri0[inodekey(m3)]].trunc? ∨ fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; new_dent := mkdentry(str0, fs0[ri0[dentrykey(ino0, str)]].ino); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).meta, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).directory, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nlink, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nsubdirs, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).size); c_inode0 := mkinode (fs0[ri0[dentrykey(ino0, str)]].ino, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .meta, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .directory, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nlink, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .size)⟫ ( ubifs-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri) ∧ orphans-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro)), fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(ino) ∈ ro, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(m3) ∈ ro, inodekey(ino0) ∈ ro

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 40:
fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], key = inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2], fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].inode?, fs0[ri0[inodekey(m3)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), 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), dentrykey(ino0, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(ino0) ∈ ri0, inodekey(ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(m3)]].trunc? ∨ fs0[ri0[inodekey(m3)]].inode? ⊦ ⟪ri[key] := adr; new_dent := mkdentry(str0, fs0[ri0[dentrykey(ino0, str)]].ino); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).meta, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).directory, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nlink, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nsubdirs, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).size); c_inode0 := mkinode (fs0[ri0[dentrykey(ino0, str)]].ino, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .meta, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .directory, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nlink, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .size)⟫ ( ubifs-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri) ∧ orphans-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro)), fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, inodekey(ino0) ∈ ro, inodekey(m3) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, inodekey(ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: data-notin-other2: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ adr0 ≠ adr1 ∧ adr0 ≠ adr2 → ¬ adr0 ∈ ri[key1, adr1][key2, adr2];%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ 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)