Theorems · Theorem · convex and discrete geometry
gaugeRescale_smul
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] (s t : Set E) {c : ℝ},
0 ≤ c → ∀ (x : E), gaugeRescale s t (c • x) = c • gaugeRescale s t x- Defined in
- Mathlib.Analysis.Convex.GaugeRescale
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- IsScalarTowerproof · cited by 3,896
- smul_smulproof · cited by 360
- mul_right_commproof · cited by 108
- gaugeproof · cited by 85
- MulActionWithZeroproof · cited by 79
- gaugeRescalestatement · cited by 12
- mul_div_mul_commproof · cited by 11
- gauge_smul_of_nonnegproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- gaugeRescale_gaugeRescaleproof · cited by 0