Theorems · Theorem · linear algebra
Module.involutive_preReflection
∀ {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}, f x = 2 → Function.Involutive ⇑(Module.preReflection x f)- Defined in
- Mathlib.LinearAlgebra.Reflection
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 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.
Cites17
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
- Module.Endstatement · cited by 774
- Module.Dualstatement and proof · cited by 583
- map_smulproof · cited by 566
- map_subproof · cited by 565
- sub_add_cancelproof · cited by 344
- sub_neg_eq_addproof · cited by 264
- smul_negproof · cited by 181
Cited by2
Results whose statement or proof uses this declaration.
- Module.reflectionproof · cited by 25
- Module.involutive_reflectionproof · cited by 3