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

⊦ ∀ 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (v0 ∈ to-vtbl(vols -- v)[v, # ebatbl] ↔ v0 ∈ to-vtbl(vols)[v, # ebatbl]) ∧ to-vtbl(vols -- v)[v, # ebatbl][v0] = to-vtbl(vols)[v, # ebatbl][v0]

Rule argument

Additional information

Used simplifier rules: to-vtbl-rec: ⊦ to-vtbl(vols[v, ebatbl]) = to-vtbl(vols -- v)[v, # ebatbl];