Theorems · Theorem · general topology
abs_dist_sub_le_dist_mul_mul
∀ {E : Type u_2} [inst : SeminormedCommGroup E] (a₁ a₂ b₁ b₂ : E), |dist a₁ b₁ - dist a₂ b₂| ≤ dist (a₁ * a₂) (b₁ * b₂)- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- absstatement and proof · cited by 1,814
- Dist.diststatement and proof · cited by 1,539
- SeminormedCommGroupstatement and proof · cited by 191
- dist_commproof · cited by 188
- abs_dist_sub_leproof · cited by 8
- dist_mul_leftproof · cited by 5
- dist_mul_rightproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AntilipschitzWith.mul_lipschitzWithproof · cited by 1