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

∀ vols0. # vols0 < # vols → true → # to-vtbl(vols0) = # vols0 ⊦ # to-vtbl(vols) = # vols

User applied rule cut formula

And obtained the following new goals

Proof step 4:
∀ vols0. # vols0 < # vols → true → # to-vtbl(vols0) = # vols0 ⊦ # to-vtbl(vols) = # vols, vols = ∅

Rule argument

fma: vols ≠ ∅

Additional information

Used simplifier rules: to-vtbl-base: ⊦ to-vtbl(∅) = ∅;% ⊦ # ∅ = 0; (s)% ⊦ # ∅ = 0; (s) Used formulas: vols ≠ ∅