Theorems · Theorem · real analysis
EReal.toENNReal_mul
∀ {x y : EReal}, 0 ≤ x → (x * y).toENNReal = x.toENNReal * y.toENNRealEReal.toENNReal is multiplicative. For the version with the nonnegativity
hypothesis on the second variable, see EReal.toENNReal_mul'.
- Defined in
- Mathlib.Data.EReal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- ENNReal.ofRealproof · cited by 863
- ERealstatement and proof · cited by 793
- Real.toERealproof · cited by 303
- lt_trichotomyproof · cited by 178
- eq_or_lt_of_leproof · cited by 92
- EReal.recproof · cited by 57
Cited by1
Results whose statement or proof uses this declaration.
- EReal.toENNReal_mul'proof · cited by 0