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Proof step 3 from proof ubifs-dir-data (previous step)

fs[ri[inodekey(ino)]].directory, ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(ino)] ∈ ri ⊦ # datakeys(inodekey(ino), ri) = 0, datakeys(inodekey(ino), ri) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 5:
fs[ri[inodekey(ino)]].directory, ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(ino)] ∈ ri ⊦ # datakeys(inodekey(ino), ri) = 0, ∀ key. key ∈ datakeys(inodekey(ino), ri) ↔ key ∈ ∅

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [∅, datakeys(inodekey(ino), ri)] flags: <all paths>

Additional information

Used terms: ∅, datakeys(inodekey(ino), ri)