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Proof step 34 from proof rename-precond-abs (previous step)

new_dent.ino = fs[ri[dentrykey(m3, new_dent.name)]].ino, inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, new_dent.dentry?, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m3, new_dent.name) ∈ ri, m3 = m4 → md = md0, inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory → new_dent.ino ≠ ROOT_INO ∧ abs-children(new_dent.ino, fs, ri) = ∅, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory, inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ boolvar ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ m7 = 0 ∧ ¬ boolvar0 ⊦ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ inodekey(new_dent.ino) ∈ ri ∧ ( ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∨ fs[ri[inodekey(new_dent.ino)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size) ∧ (fs[ri[inodekey(new_dent.ino)]].directory → dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_dent.ino ≠ ROOT_INO ∧ m0 ≠ 0 ∧ (m0 = 1 → links(new_dent.ino, fs, ri) = ∅ ++ dentrykey(m3, new_dent.name))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
inodekey(m) ∈ ri ∧ ¬ fs[ri[inodekey(m)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, m = fs[ri[dentrykey(m3, str0)]].ino, new_dent = mkdentry(str0, m), new_dent.dentry?, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m4)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m3, str0) ∈ ri, inodekey(m4) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, inodekey(m) ∈ ri ∧ fs[ri[inodekey(m)]].directory → m ≠ ROOT_INO ∧ abs-children(m, fs, ri) = ∅, m3 = m4 → md = md0, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ inodekey(m) ∈ ri ∧ ¬ fs[ri[inodekey(m)]].directory ∧ m7 = 0 ∧ ¬ boolvar0, inodekey(m) ∈ ri ∧ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar ∨ inodekey(m) ∈ ri ∧ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar, inodekey(m) ∈ ri ∧ fs[ri[inodekey(m)]].directory ∨ inodekey(m) ∈ ri ∧ ¬ fs[ri[inodekey(m)]].directory, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ inodekey(m) ∈ ri ∧ ( ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size) ∧ (fs[ri[inodekey(m)]].directory → dentrykeys(inodekey(m), ri) = ∅) ∧ m ≠ ROOT_INO ∧ m0 ≠ 0 ∧ (m0 = 1 → links(m, fs, ri) = ∅ ++ dentrykey(m3, str0))

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [new_dent, str0, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: new_dent, str0, m