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Theorems · Theorem · order theory

Order.IsPredPrelimit.lt_sub_natCast

∀ {α : Type u_1} {x y : α} [inst : PartialOrder α] [inst_1 : AddCommGroupWithOne α] [PredSubOrder α],
  Order.IsPredPrelimit x → x < y → ∀ (n : ℕ), x < y - ↑n
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderAddCommGroupWithOnePredSubOrder
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Around this declaration

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

Order.IsPredLimit.lt_sub_natCast · cited by 0IsPredLimit.lt_sub_natCastPartialOrder · cited by 6410PartialOrderOrder.IsPredPrelimit · cited by 93Order.IsPredPrelimitPredSubOrder · cited by 68PredSubOrderAddCommGroupWithOne · cited by 61AddCommGroupWithOneIsPredPrelimit.lt_sub_natCastCITED BYCITES

Cites4

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Cited by1

Results whose statement or proof uses this declaration.