Theorems · Theorem · real analysis
EReal.sign_mul_abs
∀ (x : EReal), ↑(SignType.sign x) * ↑x.abs = x
- Defined in
- Mathlib.Data.EReal.Inv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Realproof · cited by 25,697
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- one_mulproof · cited by 2,841
- absproof · cited by 1,814
- OrderHomstatement · cited by 934
- ERealstatement and proof · cited by 793
- neg_mulproof · cited by 654
- SignTypestatement and proof · cited by 318
- Real.toERealproof · cited by 303
- SignType.signstatement and proof · cited by 128
Cited by3
Results whose statement or proof uses this declaration.
- EReal.le_iff_signproof · cited by 0
- EReal.sign_eq_and_abs_eq_iff_eqproof · cited by 0
- EReal.abs_mul_signproof · cited by 0