Theorems · Theorem · group theory
Finset.sum_card_fiberwise_eq_card_filter
∀ {ι : Type u_1} {κ : Type u_5} [inst : DecidableEq κ] (s : Finset ι) (t : Finset κ) (g : ι → κ),
∑ j ∈ t, {i ∈ s | g i = j}.card = {i ∈ s | g i ∈ t}.card- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement · cited by 5,195
- Finset.cardstatement · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- Finset.filterstatement and proof · cited by 949
- Finset.card_eq_sum_onesproof · cited by 22
- Finset.sum_fiberwise_eq_sum_filterproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Finset.card_sq_le_card_mul_mulEnergyproof · cited by 1
- Finset.card_sq_le_card_mul_addEnergyproof · cited by 1