Theorems · Theorem · functional analysis
dist_eq_norm_div
∀ {E : Type u_5} [inst : SeminormedCommGroup E] (a b : E), dist a b = ‖a / b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- SeminormedCommGroup
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 and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Dist.diststatement · cited by 1,539
- SeminormedCommGroupstatement and proof · cited by 191
- div_eq_inv_mulproof · cited by 146
- dist_eq_norm_inv_mul'proof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- norm_inv_mulproof · cited by 5
- IsCompact.mul_closedBall_oneproof · cited by 4
- mem_ball_iff_norm''proof · cited by 2
- mem_closedBall_iff_norm''proof · cited by 2
- lipschitzWith_iff_norm_div_leproof · cited by 1
- tendsto_norm_div_selfproof · cited by 1
- mem_sphere_iff_norm'proof · cited by 1
- mem_ball_iff_norm'''proof · cited by 0
- edist_eq_enorm_divproof · cited by 0
- SeminormedCommGroup.mem_closure_iffproof · cited by 0
- mem_closedBall_iff_norm'''proof · cited by 0
- nndist_eq_nnnorm_divproof · cited by 0