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Proof step 190 from proof inv-unlink (previous step)

fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, fs0[ri0[inodekey(m1)]].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), 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, inodekey(ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, (adr3 = (fs0[ri0[dentrykey(m1, str)]].ino = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(m1, str)]].ino = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (fs0[ri0[dentrykey(m1, str)]].ino = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(fs0[ri0[dentrykey(m1, str)]].ino = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)]))] ) ) ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ ino = fs0[ri0[dentrykey(m1, str)]].ino ∨ inodekey(ino) ∈ ro, adr1 = adr2, adr1 = adr3, adr2 = adr3, m1 = 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 191:
fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, 1 = fs0[ri0[inodekey(m)]].nlink, fs0[ri0[dentrykey(m1, str)]] = dentrynode(key, m), links(m, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(m)]].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, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[inodekey(m1)]].size = 0, (adr3 = (m = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, false, 0, fs0[ri0[inodekey(m)]].nsubdirs, m2) ;(adr2 = (m = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (m = ino ⊃ adr3;(m1 = ino ⊃ adr1;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(m = ino ⊃ adr3;(m1 = 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, m1 = 0, fs0[ri0[inodekey(m)]].directory, inodekey(m1) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs0[ri0[dentrykey(m1, str)]], key, m]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs0[ri0[dentrykey(m1, str)]], key, m