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Proof step 5 from proof to-vtbl-update (previous step)

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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
v ∈ vols ⊦ (v0 ∈ to-vtbl(vols -- v)[v, # vols[v]] ↔ v0 ∈ vols) ∧ to-vtbl(vols -- v)[v, # vols[v]][v0] = to-vtbl(vols)[v0]

Rule argument

Additional information

Used simplifier rules: to-vtbl-in: ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols;