Theorems · Theorem · order theory
sign_nonpos_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
- 1 results in Mathlib
- Foundations
- Depth 66 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.
Cites11
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
- LT.lt.leproof · cited by 2,189
- OrderHomstatement · cited by 934
- SignTypestatement · cited by 318
- LT.lt.not_geproof · cited by 305
- lt_trichotomyproof · cited by 178
- SignType.signstatement and proof · cited by 128
- sign_posproof · cited by 49
- sign_negproof · cited by 35
- sign_zeroproof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- Real.Angle.sign_neg_coe_nonpos_of_nonneg_of_le_piproof · cited by 0