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Proof step 38 from proof refine-unlink (previous step)

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), links(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri)) = ∅ ++ alink, 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [∅ ++ alink, links(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri))] flags: <all paths>

Additional information

Used terms: ∅ ++ alink, links(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri))