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Proof step 163 from proof inv-rmdir (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), 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, inodekey(ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri0[inodekey(m0)]].size, ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ fs0[ri0[dentrykey(m0, str)]].ino = ino, fs0[ri0[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m0, str)]].ino = 0, fs0[ri0[inodekey(m0)]].nsubdirs = 0, (adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ;fs0[ri0[inodekey(ino)]] ) .nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = ri0[inodekey(ino)], adr2 = adr3, adr3 = ri0[inodekey(ino)], m0 = ino, m0 = 0, (adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ;fs0[ri0[inodekey(ino)]] ) .directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: adr1 = ri0[inodekey(ino)]

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ m ≤ n → (n - m = 0 ↔ n = m); (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss) Used formulas: adr1 = ri0[inodekey(ino)]