Mathlib Map

Theorems · Theorem · order theory

sign_apply

∀ {α : Type u_1} [inst : Zero α] [inst_1 : Preorder α] [inst_2 : DecidableLT α] {a : α},
  SignType.sign a = if 0 < a then 1 else if a < 0 then -1 else 0
Defined in
Mathlib.Data.Sign.Defs
Cited by
5 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ZeroPreorderDecidableLT
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sign_pos · cited by 49sign_possign_neg · cited by 35sign_negsign_eq_one_iff · cited by 13sign_eq_one_iffsign_eq_neg_one_iff · cited by 9sign_eq_neg_one_iffsign_eq_zero_iff · cited by 3sign_eq_zero_iffDFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderOrderHom · cited by 934OrderHomSignType · cited by 318SignTypeSignType.sign · cited by 128SignType.signsign_applyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.