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Theorems · Theorem · order theory

Order.IsSuccLimit.add_natCast_lt

∀ {α : Type u_1} {x y : α} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [SuccAddOrder α],
  Order.IsSuccLimit x → y < x → ∀ (n : ℕ), y + ↑n < x
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderAddMonoidWithOneSuccAddOrder
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Around this declaration

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

Ordinal.natCast_lt_of_isSuccLimit · cited by 3Ordinal.natCast_lt_of_isS…Order.IsSuccLimit.natCast_lt · cited by 1IsSuccLimit.natCast_ltPartialOrder · cited by 6410PartialOrderAddMonoidWithOne · cited by 313AddMonoidWithOneOrder.IsSuccLimit · cited by 255Order.IsSuccLimitSuccAddOrder · cited by 108SuccAddOrderOrder.IsSuccLimit.isSuccPrelimit · cited by 37IsSuccLimit.isSuccPrelimitOrder.IsSuccPrelimit.add_natCast_lt · cited by 1IsSuccPrelimit.add_natCas…IsSuccLimit.add_natCast_ltCITED 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.