Theorems · Theorem · real analysis
NNReal.coe_sub
∀ {r₁ r₂ : NNReal}, r₂ ≤ r₁ → ↑(r₁ - r₂) = ↑r₁ - ↑r₂- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- sub_zeroproof · cited by 938
- max_eq_leftproof · cited by 96
- le_sub_commproof · cited by 14
Cited by19
Results whose statement or proof uses this declaration.
- ENNReal.toReal_sub_of_leproof · cited by 6
- NNReal.hasSum_geometricproof · cited by 3
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- AntilipschitzWith.add_lipschitzWithproof · cited by 2
- NNReal.HolderConjugate.conjugate_eqproof · cited by 2
- summable_schlomilch_iff_of_nonnegproof · cited by 1
- cfc_tsubproof · cited by 1
- NNReal.holderConjugate_iff_eq_conjExponentproof · cited by 1
- ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mulproof · cited by 1
- AntilipschitzWith.mul_lipschitzWithproof · cited by 1
- SpectrumRestricts.nnreal_iff_spectralRadius_leproof · cited by 1