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Proof step 1 from proof to-vtbl-update-vol (conclusion)

⊦ to-vtbl(vols[v, ebatbl]) = to-vtbl(vols)[v, # ebatbl]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v])
Proof step 3:
⊦ ∀ v0. (v0 ∈ to-vtbl(vols[v, ebatbl]) ↔ v0 ∈ to-vtbl(vols)[v, # ebatbl]) ∧ to-vtbl(vols[v, ebatbl])[v0] = to-vtbl(vols)[v, # ebatbl][v0]

Rule argument

spec: store, inst: vtbl name: Extension seq: ⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v]) subst: [vtbl0, vtbl] → [to-vtbl(vols)[v, # ebatbl], to-vtbl(vols[v, ebatbl])] flags: <all paths>

Additional information

Used terms: to-vtbl(vols)[v, # ebatbl], to-vtbl(vols[v, ebatbl])