Theorems · Theorem · functional analysis
enorm_le_iff_norm_le
∀ {E : Type u_5} {F : Type u_6} [inst : SeminormedAddGroup E] [inst_1 : SeminormedAddGroup F] {x : E} {y : F},
‖x‖ₑ ≤ ‖y‖ₑ ↔ ‖x‖ ≤ ‖y‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- ENNReal.ofRealproof · cited by 863
- norm_nonnegproof · cited by 725
- ENorm.enormstatement · cited by 715
- SeminormedAddGroupstatement and proof · cited by 331
- ENNReal.ofReal_le_ofRealproof · cited by 61
- ofReal_normproof · cited by 39
- ENNReal.ofReal_le_ofReal_iffproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.HasFiniteIntegral.monoproof · cited by 7
- MeasureTheory.Integrable.measure_norm_ge_lt_topproof · cited by 3
- RCLike.lipschitzWith_improof · cited by 1
- RCLike.lipschitzWith_reproof · cited by 1