Theorems · Theorem · functional analysis
norm_sub_le_norm_sub_add_norm_sub
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a b c : E), ‖a - c‖ ≤ ‖a - b‖ + ‖b - c‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddGroupstatement and proof · cited by 331
- norm_add_leproof · cited by 68
- sub_add_sub_cancelproof · cited by 56
Cited by4
Results whose statement or proof uses this declaration.
- ODE.FunSpace.mem_closedBallproof · cited by 3
- norm_le_norm_sub_addproof · cited by 3
- norm_sub_mul_leproof · cited by 2