Theorems · Theorem · ring theory
InvariantBasisNumber.eq_of_fin_equiv
∀ {R : Type u} {inst : Semiring R} [self : InvariantBasisNumber R] {n m : ℕ} (a : (Fin n → R) ≃ₗ[R] Fin m → R), n = mAny linear equiv between Rⁿ and Rᵐ guarantees m = n.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- InvariantBasisNumber
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearEquivstatement · cited by 3,317
- InvariantBasisNumberstatement and proof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- eq_of_fin_equivproof · cited by 2