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Proof step 7 from proof to-vtbl-at (previous step)

v ∈ vols, ∀ vols0, v. # vols0 < # vols → v ∈ vols0 → to-vtbl(vols0)[v] = # vols0[v] ⊦ to-vtbl(vols)[v] = # vols[v], ∀ v. (v ∈ vols ↔ v ∈ ∅) ∧ vols[v] = (∅)[v]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
v ∈ vols, v0 ∈ vols, ∀ vols0, v. # vols0 < # vols → v ∈ vols0 → to-vtbl(vols0)[v] = # vols0[v] ⊦ to-vtbl(vols)[v] = # vols[v]

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ v ∈ vols → vols[v] = (∅)[v]; (s)% ⊦ ¬ v ∈ ∅; (s)