Theorems · Theorem · linear algebra
LinearMap.IsSymm.isRefl
∀ {R : Type u_1} {M : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {I : R →+* R}
{B : M →ₛₗ[I] M →ₗ[R] R}, B.IsSymm → B.IsRefl- Cited by
- 11 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- map_zeroproof · cited by 1,614
- LinearMap.IsSymmstatement and proof · cited by 48
- LinearMap.IsSymm.eqproof · cited by 17
- LinearMap.IsReflstatement · cited by 16
Cited by11
Results whose statement or proof uses this declaration.
- LinearMap.IsSymm.eq_iffproof · cited by 2
- LieAlgebra.IsKilling.killingForm_nondegenerateproof · cited by 2
- LinearMap.BilinForm.nondegenerate_iffproof · cited by 1
- LinearMap.IsSymm.nondegenerate_restrict_of_isCompl_kerproof · cited by 1
- RootPairing.orthogonal_rootSpan_eqproof · cited by 1
- LinearMap.BilinForm.nondegenerate_restrict_iff_disjoint_kerproof · cited by 1
- RootPairing.rootForm_nondegenerateproof · cited by 1
- LieDerivation.IsKilling.range_ad_eq_topproof · cited by 1
- LieIdeal.isCompl_killingComplproof · cited by 0
- LieAlgebra.IsKilling.traceForm_cartan_nondegenerateproof · cited by 0