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Proof step 3 from proof to-vtbl-update (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v])
Proof step 5:
v ∈ vols ⊦ ∀ v0. (v0 ∈ to-vtbl(vols -- v)[v, # vols[v]] ↔ v0 ∈ to-vtbl(vols)) ∧ to-vtbl(vols -- v)[v, # vols[v]][v0] = to-vtbl(vols)[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), to-vtbl(vols -- v)[v, # vols[v]]] flags: <all paths>

Additional information

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