Theorems · Theorem · commutative algebra
invOf_two_smul_add_invOf_two_smul
∀ {M : Type u_3} (R : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Invertible 2] (x : M), ⅟2 • x + ⅟2 • x = x- Defined in
- Mathlib.Algebra.Module.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement · cited by 268
- Convex.combo_selfproof · cited by 29
- invOf_two_add_invOf_twoproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- QuadraticMap.associated_sqproof · cited by 3
- midpoint_vsubproof · cited by 2
- IsSelfAdjoint.coe_selfAdjointPart_applyproof · cited by 2
- LieAlgebra.Orthogonal.pd_invproof · cited by 0
- StarModule.selfAdjointPart_add_skewAdjointPartproof · cited by 0
- skewAdjointPart_comp_subtype_skewAdjointproof · cited by 0