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Proof step 183 from proof inv-rmdir (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, adr = adr3, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, fs = fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], fs1 = fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], key = inodekey(fs0[ri0[dentrykey(m0, str)]].ino), key0 = dentrykey(m0, str), links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri1 -- key0, ri1 = ri0[inodekey(m0), adr1], fs0[ri0[dentrykey(m0, str)]].dentry?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, 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(m0)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ri0, dentrykey(m0, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri0[inodekey(m0)]].size, fs0[ri0[inodekey(m0)]].nsubdirs ≥ 1, fs0[ri0[inodekey(m0)]].size ≥ 1, ¬ adr ∈ ri → adr ∈ fs → adr ∈ fs, fs0[ri0[inodekey(m0)]].trunc? ∨ fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].trunc? ∨ fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].inode?, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ fs0[ri0[dentrykey(m0, str)]].ino = 0, fs0[ri0[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr])

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: data-notin-del2: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ adr0 ≠ adr1 → ¬ adr0 ∈ ri[key1, adr1] -- key2;%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)