Theorems · Theorem · order theory
self_mul_sign
∀ {α : Type u} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (x : α), x * ↑(SignType.sign x) = |x|- Defined in
- Mathlib.Data.Sign.Basic
- Cited by
- 3 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.
Cites20
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
- mul_oneproof · cited by 3,885
- IsStrictOrderedRingstatement and proof · cited by 2,490
- MulZeroClass.mul_zeroproof · cited by 2,091
- absstatement · cited by 1,814
- OrderHomstatement · cited by 934
- mul_negproof · cited by 590
- SignTypestatement · cited by 318
- lt_trichotomyproof · cited by 178
- SignType.signstatement · cited by 128
Cited by3
Results whose statement or proof uses this declaration.
- HasFDerivAt.hasFDerivAt_norm_smulproof · cited by 4
- Affine.Simplex.ExcenterExists.signedInfDist_excenterproof · cited by 3
- HasStrictFDerivAt.hasStrictFDerivAt_norm_smulproof · cited by 2