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Theorems · Theorem · order theory

Order.IsSuccLimit.natCast_lt

∀ {α : Type u_1} {x : α} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [SuccAddOrder α] [IsBotZeroClass α],
  Order.IsSuccLimit x → ∀ (n : ℕ), ↑n < x
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderAddMonoidWithOneSuccAddOrderIsBotZeroClass
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Around this declaration

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

Order.not_isSuccLimit_natCast · cited by 0Order.not_isSuccLimit_nat…PartialOrder · cited by 6410PartialOrderzero_add · cited by 2366zero_addAddMonoidWithOne · cited by 313AddMonoidWithOneOrder.IsSuccLimit · cited by 255Order.IsSuccLimitSuccAddOrder · cited by 108SuccAddOrderIsBotZeroClass · cited by 71IsBotZeroClassOrder.IsSuccLimit.pos · cited by 3IsSuccLimit.posOrder.IsSuccLimit.add_natCast_lt · cited by 2IsSuccLimit.add_natCast_ltIsSuccLimit.natCast_ltCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.