Theorems · Theorem · real analysis
Real.nnabs_of_nonneg
∀ {x : ℝ}, 0 ≤ x → Real.nnabs x = x.toNNReal- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Realstatement and proof · cited by 25,697
- NNRealstatement · cited by 4,310
- NNReal.toRealproof · cited by 1,260
- MonoidWithZeroHomstatement · cited by 704
- abs_of_nonnegproof · cited by 279
- Real.toNNRealstatement · cited by 267
- NNReal.eqproof · cited by 201
- Real.coe_toNNRealproof · cited by 27
- Real.nnabsstatement and proof · cited by 27
- Real.coe_nnabsproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- dist_anti_left_piproof · cited by 2
- dist_mono_left_piproof · cited by 1
- Real.nnabs_natCastproof · cited by 0
- Real.nnabs_coeproof · cited by 0
- Real.nnabs_ofNatproof · cited by 0
- dist_inf_sup_piproof · cited by 0