Theorems · Theorem · ring theory
card_le_of_surjective
∀ (R : Type u) [inst : Semiring R] [RankCondition R] {α : Type u_1} {β : Type u_2} [inst_2 : Fintype α]
[inst_3 : Fintype β] (f : (α → R) →ₗ[R] β → R), Function.Surjective ⇑f → Fintype.card β ≤ Fintype.card α- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- LinearEquivproof · cited by 3,317
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- Fintype.cardstatement and proof · cited by 1,386
- LinearEquiv.toLinearMapproof · cited by 1,171
- LinearEquiv.surjectiveproof · cited by 66
- Fintype.equivFinproof · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- card_le_of_surjective'proof · cited by 1