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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.

HasFPowerSeriesOnBall.congr · cited by 9HasFPowerSeriesOnBall.con…HasFiniteFPowerSeriesOnBall.cpolynomialAt_of_mem · cited by 5HasFiniteFPowerSeriesOnBa…HasFPowerSeriesOnBall.fderiv · cited by 4HasFPowerSeriesOnBall.fde…HasFPowerSeriesWithinAt.mono_of_mem_nhdsWithin · cited by 3HasFPowerSeriesWithinAt.m…HasFPowerSeriesWithinOnBall.analyticWithinAt_of_mem · cited by 3HasFPowerSeriesWithinOnBa…HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal · cited by 3HasFPowerSeriesWithinOnBa…HasFPowerSeriesOnBall.hasSum_sub · cited by 3HasFPowerSeriesOnBall.has…BoundedVariationOn.bilinear_comp · cited by 3BoundedVariationOn.biline…HasFPowerSeriesWithinOnBall.fderivWithin · cited by 2HasFPowerSeriesWithinOnBa…HasFPowerSeriesWithinOnBall.hasSum_sub · cited by 2HasFPowerSeriesWithinOnBa…HasFiniteFPowerSeriesOnBall.eq_partialSum' · cited by 2HasFiniteFPowerSeriesOnBa…HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn' · cited by 2HasFPowerSeriesWithinOnBa…eVariationOn_bilinear_comp_le · cited by 2eVariationOn_bilinear_com…OpenPartialHomeomorph.hasFPowerSeriesAt_symm · cited by 2OpenPartialHomeomorph.has…setOfPred_riemannianEDist_lt_subset_nhds · cited by 2setOfPred_riemannianEDist…Real · cited by 25697RealENNReal · cited by 9879ENNRealSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupENNReal.ofReal · cited by 863ENNReal.ofRealEDist.edist · cited by 735EDist.edistENorm.enorm · cited by 715ENorm.enormedist_dist · cited by 39edist_distofReal_norm · cited by 39ofReal_normdist_eq_norm_sub · cited by 29dist_eq_norm_subedist_eq_enorm_subCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by37

Results whose statement or proof uses this declaration.