Theorems · Theorem · ring theory
TrivSqZeroExt.inr_mul_inr
∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Module Rᵐᵒᵖ M] (m₁ m₂ : M), TrivSqZeroExt.inr m₁ * TrivSqZeroExt.inr m₂ = 0- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulOppositestatement and proof · cited by 1,135
- zero_smulproof · cited by 716
- MulOpposite.opproof · cited by 520
- TrivSqZeroExtstatement · cited by 180
- TrivSqZeroExt.inrstatement and proof · cited by 59
- TrivSqZeroExt.extproof · cited by 29
- MulOpposite.op_zeroproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- DualNumber.eps_mul_epsproof · cited by 2
- TrivSqZeroExt.isNilpotent_inrproof · cited by 1
- TrivSqZeroExt.kerIdeal_sqproof · cited by 0
- TrivSqZeroExt.lift_inlAlgHom_inrHomstatement and proof · cited by 0