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Proof step 67 from proof refine-evict (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: dir-heap-refset name: Extension seq: ⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0) subst: [ns0, ns] → [abs-keys(orphans(fs, ri1)) -- m, abs-keys (orphans (fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ abs-keys(ks) ↔ inodekey(n) ∈ ks; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ ¬ inodekey(m).data?; (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (s)% ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]); (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ino ∈ ns -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ ns; (s) Used terms: abs-keys(orphans(fs, ri1)) -- m, abs-keys (orphans(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)))