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Proof step 9 from proof to-vtbl-update-vol (previous step)

⊦ to-vtbl(vols -- v)[v0] = to-vtbl(vols)[v0], v0 = v, v0 ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ¬ v ∈ vtbl → vtbl[v] = (∅)[v]
Proof step 11:
⊦ (∅)[v0] = to-vtbl(vols)[v0], v0 = v, v0 ∈ vols, v0 ∈ to-vtbl(vols -- v)

Rule argument

spec: store, inst: vtbl name: notmemlookup seq: ⊦ ¬ v ∈ vtbl → vtbl[v] = (∅)[v] subst: [v, vtbl] → [v0, to-vtbl(vols -- v)] flags: <all paths>

Additional information

Used simplifier rules: to-vtbl-in: ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols;% ⊦ v ∈ vols -- v0 ↔ v ≠ v0 ∧ v ∈ vols; (s) Used terms: v0, to-vtbl(vols -- v)