Theorems · Theorem · general topology
dist_sub_sub_le
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] (a₁ a₂ b₁ b₂ : E), dist (a₁ - a₂) (b₁ - b₂) ≤ dist a₁ b₁ + dist a₂ b₂- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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.
- Realstatement · cited by 25,697
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement and proof · cited by 1,539
- sub_eq_add_negproof · cited by 1,023
- dist_add_add_leproof · cited by 4
- dist_neg_negproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- dist_sub_sub_le_of_leproof · cited by 0