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Proof step 4 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]

User applied rule cut formula

And obtained the following new goals

Proof step 5:
v ∈ vols, ∀ vols0, v. # vols0 < # vols → v ∈ vols0 → to-vtbl(vols0)[v] = # vols0[v] ⊦ to-vtbl(vols)[v] = # vols[v], vols = ∅

Rule argument

fma: vols = ∅

Additional information

Used simplifier rules: to-vtbl-base: ⊦ to-vtbl(∅) = ∅;% ⊦ ¬ v ∈ ∅; (s) Used formulas: vols = ∅