Theorems · Theorem · functional analysis
edist_eq_enorm_sub
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (a b : E), edist a b = ‖a - b‖ₑ- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 147 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ENNReal.ofRealproof · cited by 863
- EDist.ediststatement · cited by 735
- ENorm.enormstatement and proof · cited by 715
- edist_distproof · cited by 39
- ofReal_normproof · cited by 39
- dist_eq_norm_subproof · cited by 29
Cited by37
Results whose statement or proof uses this declaration.
- HasFPowerSeriesOnBall.congrproof · cited by 9
- HasFiniteFPowerSeriesOnBall.cpolynomialAt_of_memproof · cited by 5
- HasFPowerSeriesOnBall.fderivproof · cited by 4
- HasFPowerSeriesWithinAt.mono_of_mem_nhdsWithinproof · cited by 3
- HasFPowerSeriesWithinOnBall.analyticWithinAt_of_memproof · cited by 3
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- HasFPowerSeriesOnBall.hasSum_subproof · cited by 3
- BoundedVariationOn.bilinear_compproof · cited by 3
- HasFPowerSeriesWithinOnBall.fderivWithinproof · cited by 2
- HasFPowerSeriesWithinOnBall.hasSum_subproof · cited by 2
- HasFiniteFPowerSeriesOnBall.eq_partialSum'proof · cited by 2
- HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn'proof · cited by 2