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Proof step 210 from proof inv-unlink (previous step)

m3 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], fs1 = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], fs2 = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], key = inodekey(fs0[ri0[dentrykey(m1, str)]].ino), key0 = dentrykey(m1, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', log2 = ((log0 + adr1 ') + adr2 ') + adr3 ', m = fs0[ri0[dentrykey(m1, str)]].ino, ri = ri2[key, adr], ri1 = ri0[inodekey(m1), adr1], ri2 = ri1 -- key0, fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).inode?, fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), key-cons(key, fs[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), adr ∈ fs, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].size ≥ 1, ¬ adr ∈ ri2 → adr ∈ fs → adr ∈ fs, m3 = 0 → links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).trunc? ∨ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).inode?, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO, fs0[ri0[inodekey(m1)]].trunc? ∨ fs0[ri0[inodekey(m1)]].inode? ⊦ ⟪c_inode0 := mkinode (m, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).meta, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) .directory, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).nlink, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).size)⟫ (ubifs-cons(fs1, ri, ro, fi, fo, log1) ∧ replay-cons-strong(fs1, ri, ro, fi, fo, log1) ∧ file-node-cons(fs1, ri) ∧ orphans-cons(fs1, ri, ro)), fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m1 = 0, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro, adr ∈ ri2

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 211:
m3 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], fs1 = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], fs2 = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], key = inodekey(fs0[ri0[dentrykey(m1, str)]].ino), key0 = dentrykey(m1, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', log2 = ((log0 + adr1 ') + adr2 ') + adr3 ', m = fs0[ri0[dentrykey(m1, str)]].ino, ri = ri2[key, adr], ri1 = ri0[inodekey(m1), adr1], ri2 = ri1 -- key0, fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, fs0[ri0[inodekey(m1)]].inode?, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), key-cons(key, fs[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), dentrykey(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, adr ∈ fs, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].size ≥ 1, m3 = 0 → links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), ¬ adr ∈ ri2 → adr ∈ fs → adr ∈ fs, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).trunc? ∨ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).inode?, fs0[ri0[inodekey(m1)]].trunc? ∨ fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).trunc? ∨ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).inode? ⊦ fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m1 = 0, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr ∈ ri2, inodekey(m1) ∈ ro, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ubifs-cons(fs1, ri, ro, fi, fo, log1) ∧ replay-cons-strong(fs1, ri, ro, fi, fo, log1) ∧ file-node-cons(fs1, ri) ∧ orphans-cons(fs1, ri, ro)

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);%data-notin-del2: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ adr0 ≠ adr1 → ¬ adr0 ∈ ri[key1, adr1] -- key2;%dentry-ubifs-cons: ⊦ dentrykey(ino, str) ∈ ri ∧ ri[dentrykey(ino, str)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[dentrykey(ino, str)]].dentry?;%inode-ubifs-cons: ⊦ inodekey(ino) ∈ ri ∧ ri[inodekey(ino)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].inode?;% ⊦ n ≥ m ↔ m ≤ n; (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)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).trunc?; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)