Theorems · Theorem · order theory
sign_mul_abs
∀ {α : Type u} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (x : α), ↑(SignType.sign x) * |x| = x- Defined in
- Mathlib.Data.Sign.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 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 · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- one_mulproof · cited by 2,841
- IsStrictOrderedRingstatement and proof · cited by 2,490
- MulZeroClass.mul_zeroproof · cited by 2,091
- absstatement · cited by 1,814
- neg_negproof · cited by 960
- OrderHomstatement · cited by 934
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- SignTypestatement · cited by 318
Cited by2
Results whose statement or proof uses this declaration.
- EReal.sign_mul_absproof · cited by 3
- hasSum_mellin_pi_mul_sq'proof · cited by 2