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Proof step 45 from proof refine-evict (previous step)

fs[ri1[inodekey(m)]].nlink = 0, fs[ri1[inodekey(m)]].directory, fs[ri1[inodekey(ino)]].directory, orphans(fs, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri1) -- m, abs-files(fs, ri1)), afs-cons(abs-dirs(fs, ri1), abs-files(fs, ri1)), file-node-cons(fs, ri1), log-cons(log, fs), orphans-cons(fs, ri1, orphans(fs, ri1)), replay-cons-strong(fs, ri1, orphans(fs, ri1), fi, fo, log), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs, ri1, orphans(fs, ri1), fi, fo, log), inodekey(m) ∈ ri1, dentrykey(ino, str) ∈ ri1, inodekey(ino) ∈ ri1, asynced → boolvar1, ∀ ino. inodekey(ino) ∈ ri1 ∧ fs[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO → links(ino, fs, ri1) = ∅, ∀ ino. inodekey(ino) ∈ ri1 ∧ fs[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO → dentrykeys(inodekey(ino), ri1) = ∅ ⊦ abs-children(ino, fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m))[str] = fs[ri1[dentrykey(ino, str)]].ino, ino = m, m = ROOT_INO

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-abs name: at-children seq: ⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino subst: [ino, str, ri, fs] → [ino, str, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), fs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (s)% ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]); (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ ¬ dentrykey(m, str).data?; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls) Used terms: ino, str, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), fs