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Theorems · Theorem · real analysis

NNReal.coe_inj

∀ {r₁ r₂ : NNReal}, ↑r₁ = ↑r₂ ↔ r₁ = r₂
Defined in
Mathlib.Data.NNReal.Defs
Cited by
30 results in Mathlib
Foundations
Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NNReal.coe_eq_zero · cited by 11NNReal.coe_eq_zeroEisensteinSeries.norm_eq_max_natAbs · cited by 8EisensteinSeries.norm_eq_…NNReal.coe_eq_one · cited by 5NNReal.coe_eq_oneProbabilityTheory.gaussianReal_map_const_mul · cited by 4ProbabilityTheory.gaussia…IsUltrametricDist.nnnorm_add_eq_max_of_nnnorm_ne_nnnorm · cited by 2IsUltrametricDist.nnnorm_…NNReal.iInf_mul · cited by 2NNReal.iInf_mulNNReal.mul_iSup · cited by 2NNReal.mul_iSupReal.toNNReal_prod_of_nonneg · cited by 1Real.toNNReal_prod_of_non…Real.toNNReal_sum_of_nonneg · cited by 1Real.toNNReal_sum_of_nonn…ContinuousLinearMap.opNNNorm_lsmul · cited by 1ContinuousLinearMap.opNNN…ContinuousLinearMap.opNNNorm_lsmul_apply · cited by 1ContinuousLinearMap.opNNN…NNReal.pow_rpow_inv_natCast · cited by 1NNReal.pow_rpow_inv_natCa…Real.geom_mean_le_arith_mean2_weighted · cited by 1Real.geom_mean_le_arith_m…MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner · cited by 1MeasureTheory.eLpNorm_le_…NNReal.rpow_eq_zero_iff · cited by 1NNReal.rpow_eq_zero_iffReal · cited by 25697RealNNReal · cited by 4310NNRealNNReal.toReal · cited by 1260NNReal.toRealNNReal.coe_injective · cited by 16NNReal.coe_injectiveNNReal.coe_injCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by30

Results whose statement or proof uses this declaration.