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Theorems · Theorem · number theory

Finset.mulEnergy_empty_left

∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Mul α] (t : Finset α), ∅.mulEnergy t = 0
Defined in
Mathlib.Combinatorics.Additive.Energy
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.mulEnergy_pos_iff · cited by 1Finset.mulEnergy_pos_iffFinset · cited by 13712FinsetFinset.card · cited by 2327Finset.cardSProd.sprod · cited by 1750SProd.sprodFinset.filter.congr_simp · cited by 47filter.congr_simpFinset.filter_empty · cited by 23Finset.filter_emptyFinset.mulEnergy · cited by 22Finset.mulEnergyFinset.product_empty · cited by 7Finset.product_emptyFinset.mulEnergy_empty_leftCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.