Theorems · Theorem · functional analysis
nndist_eq_nnnorm_neg_add
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a b : E), nndist a b = ‖-a + b‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 114 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- NNDist.nndiststatement · cited by 235
- NNReal.eqproof · cited by 201
- dist_eq_norm_neg_addproof · cited by 46
Cited by3
Results whose statement or proof uses this declaration.
- nontrivialTopology_iff_exists_nnnorm_ne_zeroproof · cited by 4
- nndist_zero_rightproof · cited by 4
- nndist_zero_leftproof · cited by 1