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Proof step 62 from proof refine-evict (previous step)

fs[ri1[inodekey(m)]].nlink = 0, fs[ri1[inodekey(ino)]].directory, orphans(fs, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri1), abs-files(fs, ri1) -- m), 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, 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-dirs(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m))[ino] = mkdir (fs[ri1[inodekey(ino)]].size, fs[ri1[inodekey(ino)]].meta, fs[ri1[inodekey(ino)]].nlink, fs[ri1[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri1)), m = ROOT_INO, fs[ri1[inodekey(m)]].directory

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: mkdir-inj: ⊦ mkdir(n, md, m, n0, entries0) = mkdir(n, md, m, n0, entries1) ↔ entries0 = entries1;%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (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)% ⊦ ¬ inodekey(m).data?; (s)%⊦ entries = abs-children(ino, fs, ri) ↔ (∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ ( str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino)); (ss)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)% ⊦ ¬ dentrykey(m, str).data?; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s) Used terms: ino, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), fs