Theorems · Theorem · functional analysis
enorm_le_coe
∀ {E : Type u_8} [inst : NNNorm E] {x : E} {r : NNReal}, ‖x‖ₑ ≤ ↑r ↔ ‖x‖₊ ≤ r- Defined in
- Mathlib.Analysis.Normed.Group.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NNNorm
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.
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- ENNReal.ofNNRealstatement · cited by 1,279
- NNNorm.nnnormstatement and proof · cited by 952
- ENorm.enormstatement · cited by 715
- NNNormstatement and proof · cited by 33
Cited by3
Results whose statement or proof uses this declaration.
- div_le_egauge_closedBallproof · cited by 2
- HasFPowerSeriesWithinAt.compproof · cited by 2
- HasFPowerSeriesAt.tendsto_partialSum_prod_of_compproof · cited by 1