Theorems · Definition · field theory
DilationEquiv.mulLeft
{α : Type u_1} → [inst : NormedDivisionRing α] → (a : α) → a ≠ 0 → α ≃ᵈ αMultiplication by a nonzero element a on the left
as a DilationEquiv of a normed division ring.
- Defined in
- Mathlib.Analysis.Normed.Field.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- NormedDivisionRingstatement and proof · cited by 360
- DilationEquivstatement · cited by 55
- Dilationproof · cited by 44
- Equiv.mulLeft₀proof · cited by 6
- Dilation.mulLeftproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Filter.map_mul_left_coboundedproof · cited by 1
- DilationEquiv.mulLeft_symm_applystatement · cited by 0
- DilationEquiv.mulLeft_applystatement and proof · cited by 0