Theorems · Theorem · real analysis
NNReal.coe_sInf
∀ (s : Set NNReal), ↑(sInf s) = sInf (NNReal.toReal '' s)
- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.imagestatement and proof · cited by 5,609
- NNRealstatement and proof · cited by 4,310
- Set.Nonemptyproof · cited by 2,627
- NNReal.toRealstatement and proof · cited by 1,260
- Set.Iciproof · cited by 1,070
- InfSet.sInfstatement and proof · cited by 935
- Set.eq_empty_or_nonemptyproof · cited by 248
- Set.image_emptyproof · cited by 73
- OrderBot.bddBelowproof · cited by 31
- Real.sInf_emptyproof · cited by 21
Cited by5
Results whose statement or proof uses this declaration.
- NNReal.coe_iInfproof · cited by 4
- NNReal.sInf_emptyproof · cited by 2
- ContinuousLinearMap.nnnorm_defproof · cited by 1
- ENNReal.toReal_sInfproof · cited by 0
- BoundedContinuousFunction.nndist_eqproof · cited by 0