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Proof step 47 from proof inv-evict (previous step)

replay-log(log, fs, fi ⊖ fo) = ri1 ⊖ ro0, ro0.inodes?, fo.inodes?, file-node-cons(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)), file-node-cons(fs, ri1), log-cons(log, fs), orphans-cons(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), ro0 -- inodekey(m)), orphans-cons(fs, ri1, ro0), replay-safe(log, fs, fi ⊖ fo), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs, ri1, ro0, fi, fo, log), inodekey(m) ∈ ro0, inodekey(m) ∈ ri1, ∀ ino. inodekey(ino) ∈ ro0 → dentrykeys(inodekey(ino), ri1) = ∅, ∀ ino. inodekey(ino) ∈ ro0 → links(ino, fs, ri1) = ∅ ⊦ # ro0 = 0, (ri1 ⊖ ro0)[key] = (inodekey(m) = key ⊃ (∅)[inodekey(m)] ;( key ∈ datakeys(ro0, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) \ datakeys(inodekey(m), (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ⊃ (∅)[key] ;(key ∈ ro0 ⊃ (∅)[key];(key ∈ ri1 ∧ key.data? ∧ key.ino = m ⊃ (∅)[key];ri1[key])) ) ), m = ROOT_INO, ro0 = ∅, key ∈ ri1 ∧ ¬ key ∈ ro0 ∧ ¬ key.data?

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: dels-with-data seq: ⊦ ri ⊖ ks = (ri \ ks) \ datakeys(ks, ri) subst: [ks, ri] → [ro0, ri1] flags: <all paths>

Additional information

Used terms: ro0, ri1