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

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

User applied rule induction

And obtained the following new goals

Proof step 4:
v ∈ vols, ∀ vols0, v. # vols0 < # vols → v ∈ vols0 → to-vtbl(vols0)[v] = # vols0[v] ⊦ to-vtbl(vols)[v] = # vols[v]

Rule argument

indvar: # vols wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # vols