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Proof step 166 from proof inv-rmdir (previous step)

fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, 1 = fs0[ri0[inodekey(m)]].nlink, fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m), dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m0, str), fs0[ri0[dentrykey(m0, str)]].dentry?, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(m0)]].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), inodekey(ino) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m0)]].size, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, (adr3 = (m = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, 0, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ;(adr2 = (m = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), 0) ;(adr1 = (m = ino ⊃ adr3;(m0 = ino ⊃ 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[(m = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri0[inodekey(ino)]))] ) ) ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ ino = m ∨ inodekey(ino) ∈ ro, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m = ROOT_INO, m0 = 0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, 1 = fs0[ri0[inodekey(m)]].nlink, fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m), dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m0, str), fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(m)]].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(m)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri0[inodekey(m0)]].size, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, (adr3 = (m = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, 0, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ;(adr2 = (m = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), 0) ;(adr1 = (m = ino ⊃ adr3;(m0 = ino ⊃ 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[(m = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri0[inodekey(ino)]))] ) ) ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ ino = m ∨ inodekey(ino) ∈ ro, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = ROOT_INO, m = 0, m0 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m) ∈ ro

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)% ⊦ dentrynode(key, m).dentry?; (s)%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]