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Proof step 2 from proof count-entries (previous step)

∀ str. str ∈ entries ↔ str ∈ sdt, ∀ entries0, sdt. # entries0 < # entries → (∀ str. str ∈ entries0 ↔ str ∈ sdt) → # entries0 = # sdt ⊦ # entries = # sdt

User applied rule cut formula

And obtained the following new goals

Proof step 3:
entries = ∅, ∀ str. str ∈ entries ↔ str ∈ sdt, ∀ entries0, sdt. # entries0 < # entries → (∀ str. str ∈ entries0 ↔ str ∈ sdt) → # entries0 = # sdt ⊦ # entries = # sdt
Proof step 8:
∀ str. str ∈ entries ↔ str ∈ sdt, ∀ entries0, sdt. # entries0 < # entries → (∀ str. str ∈ entries0 ↔ str ∈ sdt) → # entries0 = # sdt ⊦ # entries = # sdt, entries = ∅

Rule argument

fma: entries = ∅

Additional information

Used formulas: entries = ∅