Mathlib Map

Theorems · Theorem · order theory

Order.covBy_iff_add_one_eq

∀ {α : Type u_1} {x y : α} [inst : PartialOrder α] [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α] [NoMaxOrder α],
  x ⋖ y ↔ x + 1 = y
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderAddOneSuccAddOrderNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Int.natCast_covBy · cited by 1Int.natCast_covByNat.covBy_iff_add_one_eq · cited by 0Nat.covBy_iff_add_one_eqPartialOrder · cited by 6410PartialOrderNoMaxOrder · cited by 340NoMaxOrderCovBy · cited by 290CovByOrder.succ_eq_add_one · cited by 115Order.succ_eq_add_oneSuccAddOrder · cited by 108SuccAddOrderOrder.succ_eq_iff_covBy · cited by 3Order.succ_eq_iff_covByOrder.covBy_iff_add_one_eqCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.