Theorems · Theorem · order theory
sign_eq_zero_iff
∀ {α : Type u_1} [inst : Zero α] [inst_1 : LinearOrder α] {a : α}, SignType.sign a = 0 ↔ a = 0- Defined in
- Mathlib.Data.Sign.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LinearOrderstatement and proof · cited by 8,572
- OrderHomstatement · cited by 934
- le_of_not_gtproof · cited by 430
- SignTypestatement and proof · cited by 318
- SignType.signstatement and proof · cited by 128
- sign_zeroproof · cited by 33
- LE.le.eq_of_not_ltproof · cited by 25
- SignType.ctorIdxproof · cited by 11
- sign_applyproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Real.Angle.sign_eq_zero_iffproof · cited by 7
- Affine.Simplex.ExcenterExists.touchpoint_ne_pointproof · cited by 1
- sign_ne_zeroproof · cited by 1