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

∀ vols0, v. # vols0 < # vols → true → (v ∈ to-vtbl(vols0) ↔ v ∈ vols0) ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: vols = ∅

Additional information

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