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Proof step 479 from proof inv-rename-overwrite-keep-parent (previous step)

m8 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)]].nlink, m0 + 1 = fs0[ri0[inodekey(m)]].size, n0 + (boolvar3 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)]].directory ↔ ¬ boolvar0, fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str0)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)]].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), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(m, str0)]].ino) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), m8 = 0 → links(fs0[ri0[dentrykey(m, str0)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str0), fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)]].directory → dentrykeys(inodekey(fs0[ri0[dentrykey(m, str0)]].ino), ri0) = ∅, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)]].directory ∧ boolvar2 ∧ m6 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str0)]].ino)]].size ⊦ fs0[ri0[dentrykey(m, str0)]].ino = 0, fs0[ri0[dentrykey(m, str0)]].ino = ROOT_INO, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, mkdentry(str, m2) = mkdentry(str0, fs0[ri0[dentrykey(m, str0)]].ino), inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 480:
n0 + (boolvar3 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, m0 + 1 = fs0[ri0[inodekey(m)]].size, m8 + 1 = fs0[ri0[inodekey(m1)]].nlink, ¬ fs0[ri0[inodekey(m1)]].directory ↔ ¬ boolvar0, fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key, m1), fs0[ri0[dentrykey(m, str0)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(m1)]].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), adr2 ∈ ri0 -- dentrykey(m, str), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, fs0[ri0[inodekey(m1)]].directory → dentrykeys(inodekey(m1), ri0) = ∅, m8 = 0 → links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), ¬ boolvar0 ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m1)]].directory ∧ boolvar2 ∧ m6 = fs0[ri0[inodekey(m1)]].size, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m1 = ROOT_INO, m1 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro

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(m, str0)]], key, m1]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs0[ri0[dentrykey(m, str0)]], key, m1