Theorems · Theorem · ring theory
Unitization.inr_smul
∀ {S : Type u_2} (R : Type u_3) {A : Type u_4} [inst : Zero R] [inst_1 : SMulZeroClass S R] [inst_2 : SMul S A] (r : S)
(m : A), ↑(r • m) = r • ↑m- Defined in
- Mathlib.Algebra.Algebra.Unitization
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- ZeroSMulZeroClassSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- smul_zeroproof · cited by 665
- Unitizationstatement · cited by 220
- SMulZeroClassstatement and proof · cited by 213
- Unitization.inrstatement · cited by 109
- Unitization.extproof · cited by 21
Cited by8
Results whose statement or proof uses this declaration.
- Unitization.quasispectrum_eq_spectrum_inr'proof · cited by 12
- Unitization.quasispectrum_eq_spectrum_inrproof · cited by 4
- Unitization.convexOn_of_convexOn_inr_compproof · cited by 1
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- Unitization.inl_mul_inrproof · cited by 0
- Unitization.inr_mul_inlproof · cited by 0
- Unitization.concaveOn_of_concaveOn_inr_compproof · cited by 0