Theorems · Theorem · commutative algebra
Finset.cast_card
∀ {α : Type u_3} {R : Type u_5} [inst : NonAssocSemiring R] (s : Finset α), ↑s.card = ∑ x ∈ s, 1- Defined in
- Mathlib.Algebra.Module.BigOperators
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 2,327
- NonAssocSemiringstatement and proof · cited by 805
- Finset.sum_constproof · cited by 254
- Nat.smul_one_eq_castproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- Finset.exists_le_card_fiber_of_nsmul_le_card_of_maps_toproof · cited by 3
- Finset.exists_card_fiber_le_of_card_le_nsmulproof · cited by 2
- Finset.exists_card_fiber_lt_of_card_lt_nsmulproof · cited by 2
- Finset.exists_lt_card_fiber_of_nsmul_lt_card_of_maps_toproof · cited by 2
- jacobiSum_trivial_trivialproof · cited by 1