Theorems · Theorem · number theory
WithZeroMulInt.toNNReal_strictMono
∀ {e : NNReal} (he : 1 < e), StrictMono ⇑(WithZeroMulInt.toNNReal ⋯)The map toNNReal is strictly monotone whenever 1 < e.
- Defined in
- Mathlib.Data.Int.WithZero
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 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.
- DFunLike.coestatement and proof · cited by 62,936
- NNRealstatement and proof · cited by 4,310
- map_zeroproof · cited by 1,614
- Multiplicativestatement and proof · cited by 875
- StrictMonostatement · cited by 706
- MonoidWithZeroHomstatement · cited by 704
- WithZerostatement and proof · cited by 586
- WithZero.coeproof · cited by 186
- Multiplicative.toAddproof · cited by 161
- WithZero.unzeroproof · cited by 38
- LT.lt.ne_zerostatement and proof · cited by 34
- LT.lt.posproof · cited by 30
Cited by4
Results whose statement or proof uses this declaration.
- WithZeroMulInt.toNNReal_lt_one_iffproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbvDefproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbvDefproof · cited by 1
- WithZeroMulInt.toNNReal_le_one_iffproof · cited by 1