Theorems · Theorem · nonassociative algebras
RootPairing.RootPositiveForm.isOrthogonal_reflection
∀ {ι : Type u_1} {R : Type u_2} {S : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommRing S]
[inst_1 : LinearOrder S] [inst_2 : CommRing R] [inst_3 : Algebra S R] [inst_4 : AddCommGroup M] [inst_5 : Module R M]
[inst_6 : AddCommGroup N] [inst_7 : Module R N] {P : RootPairing ι R M N} [inst_8 : P.IsValuedIn S]
(self : RootPairing.RootPositiveForm S P) (i : ι), LinearMap.IsOrthogonal self.form ⇑(P.reflection i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearOrderstatement and proof · cited by 8,572
- LinearEquivstatement · cited by 3,317
- RootPairingstatement and proof · cited by 710
- RootPairing.IsValuedInstatement and proof · cited by 108
- RootPairing.reflectionstatement · cited by 79
- RootPairing.RootPositiveFormstatement and proof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.RootPositiveForm.toInvariantFormproof · cited by 11