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Proof step 34 from proof refine-unlink (previous step)

# links(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri)) = 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(ROOT_INO)]].directory, fo.inodes?, orphans(fs, ri).inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), 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(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, inodekey(ROOT_INO) ∈ ri, asynced → boolvar, ∀ name. dentrykey(fs[ri[dentrykey(m, str)]].ino, name) ∈ ri → inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino].entries[name]) ∈ ri ∧ fs[ri[inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino].entries[name])]].directory ∨ inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino].entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino].entries[name])]].directory, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
# links(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri)) = 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1, abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino] = mkdir(m0, md, m1, m2, entries), fs[ri[inodekey(ROOT_INO)]].directory, fs[ri[inodekey(m)]].directory, orphans(fs, ri).inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), 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), inodekey(ROOT_INO) ∈ ri, dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, inodekey(m) ∈ ri, asynced → boolvar, ∀ name. dentrykey(fs[ri[dentrykey(m, str)]].ino, name) ∈ ri → inodekey(entries[name]) ∈ ri ∧ fs[ri[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(entries[name])]].directory, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino], m0, md, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dirs(fs, ri)[fs[ri[dentrykey(m, str)]].ino], m0, md, m1, m2, entries