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Proof step 123 from proof inv-link (previous step)

fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO ↔ inodekey(ino1) ∈ ro, fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino, str)]].ino), fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].inode?, fs0[ri0[inodekey(m3)]].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(ino1) ∈ ri0, dentrykey(ino0, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(ino0) ∈ ri0, inodekey(ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs0[ri0[dentrykey(ino, str)]].ino = 0, (adr3 = (fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino, str)]].ino) ;(adr1 = (fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)])) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)]))] ) ) ) .nlink = 0 ∧ ino1 ≠ ROOT_INO ↔ inodekey(ino1) ∈ ro, adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].directory, inodekey(ino0) ∈ ro, inodekey(m3) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ro, inodekey(ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 124:
fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO ↔ inodekey(ino1) ∈ ro, fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino, str)]].ino), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar, m, m0, m1), boolvar, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, 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(m3)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)] ∈ fs0, inodekey(ino) ∈ ri0, inodekey(ino0) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(ino0, str) ∈ ri0, inodekey(ino1) ∈ ri0, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, m ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ fs0[ri0[dentrykey(ino, str)]].ino = 0, (adr3 = (fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino, str)]].ino) ;(adr1 = (fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)])) ⊃ inodenode(inodekey(m3), md0, true, m, m0, m1 + 1) ;fs0[(fs0[ri0[dentrykey(ino, str)]].ino = ino1 ⊃ adr3;(m3 = ino1 ⊃ adr1;ri0[inodekey(ino1)]))] ) ) ) .nlink = 0 ∧ ino1 ≠ ROOT_INO ↔ inodekey(ino1) ∈ ro, adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(ino) ∈ ro, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(m3) ∈ ro, inodekey(ino0) ∈ ro

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs0[ri0[inodekey(m3)]], key0, md1, boolvar, m, m0, m1]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs0[ri0[inodekey(m3)]], key0, md1, boolvar, m, m0, m1