Theorems · Theorem · linear algebra
Module.involutive_reflection
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {x : M}
{f : Module.Dual R M} (h : f x = 2), Function.Involutive ⇑(Module.reflection h)- Defined in
- Mathlib.LinearAlgebra.Reflection
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- 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
- LinearEquivstatement · cited by 3,317
- Module.Dualstatement and proof · cited by 583
- Function.Involutivestatement · cited by 103
- Module.reflectionstatement · cited by 25
- Module.involutive_preReflectionproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.reflection_sameproof · cited by 2
- Module.invOn_reflection_of_mapsToproof · cited by 1
- RootPairing.coreflection_sameproof · cited by 0