Theorems · Theorem · ring theory
Unitization.inr_mul
∀ (R : Type u_1) {A : Type u_2} [inst : MulZeroClass R] [inst_1 : AddZeroClass A] [inst_2 : Mul A]
[inst_3 : SMulWithZero R A] (a₁ a₂ : A), ↑(a₁ * a₂) = ↑a₁ * ↑a₂- Defined in
- Mathlib.Algebra.Algebra.Unitization
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- AddZeroClassstatement and proof · cited by 1,237
- zero_smulproof · cited by 716
- MulZeroClassstatement and proof · cited by 232
- Unitizationstatement · cited by 220
- SMulWithZerostatement and proof · cited by 113
- Unitization.inrstatement and proof · cited by 109
- Unitization.toProdproof · cited by 76
- Unitization.extproof · cited by 21
Cited by9
Results whose statement or proof uses this declaration.
- CommCStarAlgebra.norm_add_eq_maxproof · cited by 3
- quasispectrum.mul_commproof · cited by 3
- SemiconjBy.star_rightproof · cited by 2
- Unitization.isQuasiregular_inr_iffproof · cited by 2
- CStarAlgebra.spectralOrderedRingproof · cited by 1
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- CStarAlgebra.norm_sub_mul_self_le_of_inrproof · cited by 0
- Unitization.sqrt_inrproof · cited by 0