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Proof step 537 from proof inv-rename-overwrite-reparent (previous step)

¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(m)]].directory, ro.inodes?, fo.inodes?, fs[ri[inodekey(m)]].nsubdirs < (boolvar3 ⊃ 1;0), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[dentrykey(m, str)] ∈ fs, inodekey(m0) ∈ ri, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m0, str0)]].ino) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m0, str0)]].ino), ri) = ∅, m5 = 1 → links(fs[ri[dentrykey(m0, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str0), boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ fs[ri[dentrykey(m0, str0)]].ino = ROOT_INO, fs[ri[inodekey(m)]].size = 0, m0 = m, m5 = 0, inodekey(m0) ∈ ro, inodekey(m) ∈ ro

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 538:
¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(m1)]].directory, fs[ri[dentrykey(m, str)]] = dentrynode(key, m1), fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, fs[ri[inodekey(m)]].nsubdirs < (boolvar3 ⊃ 1;0), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), dentrykey(m, str) ∈ ri, inodekey(m1) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(fs[ri[dentrykey(m0, str0)]].ino) ∈ ri, inodekey(m) ∈ ri, inodekey(m0) ∈ ri, ri[dentrykey(m, str)] ∈ fs, 1 ≤ fs[ri[inodekey(m)]].size, boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, m5 = 1 → links(fs[ri[dentrykey(m0, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str0), fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m0, str0)]].ino), ri) = ∅, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ fs[ri[inodekey(m1)]].directory ∧ ¬ boolvar3 ∧ m2 = fs[ri[inodekey(m1)]].nlink ∧ m3 = fs[ri[inodekey(m1)]].nsubdirs ∨ fs[ri[inodekey(m1)]].directory ∧ boolvar3 ∧ m2 = fs[ri[inodekey(m1)]].nlink ∧ m3 = fs[ri[inodekey(m1)]].nsubdirs ∧ m4 = fs[ri[inodekey(m1)]].size, ¬ fs[ri[inodekey(m1)]].directory ∧ ¬ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].size ⊦ fs[ri[dentrykey(m0, str0)]].ino = ROOT_INO, fs[ri[inodekey(m)]].size = 0, m0 = m, m5 = 0, inodekey(m) ∈ ro, inodekey(m0) ∈ 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] → [fs[ri[dentrykey(m, str)]], key, m1]

Additional information

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