Theorems · Theorem · linear algebra
LinearMap.IsPerfPair.bijective_left
∀ {R : Type u_1} {M : Type u_3} {N : Type u_5} {inst : AddCommGroup M} {inst_1 : AddCommGroup N} {inst_2 : CommRing R}
{inst_3 : Module R M} {inst_4 : Module R N} (p : M →ₗ[R] N →ₗ[R] R) [self : p.IsPerfPair], Function.Bijective ⇑p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Quot.sound
- Assumes
- LinearMap.IsPerfPair
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Function.Bijectivestatement · cited by 863
- LinearMap.IsPerfPairstatement and proof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.toPerfPairproof · cited by 46
- LinearMap.IsPerfPair.flipproof · cited by 1