Theorems · Theorem · real analysis
Real.lt_toNNReal_iff_coe_lt
∀ {r : NNReal} {p : ℝ}, r < p.toNNReal ↔ ↑r < p- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 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 and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- Real.toNNRealstatement · cited by 267
- lt_iff_lt_of_le_iff_leproof · cited by 54
- Real.toNNReal_le_iff_le_coeproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.lt_ofReal_iff_toReal_ltproof · cited by 7
- spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smulproof · cited by 1