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Theorems · Theorem · order theory

Order.IsSuccPrelimit.add_natCast_lt

∀ {α : Type u_1} {x y : α} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [SuccAddOrder α],
  Order.IsSuccPrelimit x → y < x → ∀ (n : ℕ), y + ↑n < x
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
1 results in Mathlib
Foundations
Depth 17 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.

Order.IsSuccLimit.add_natCast_lt · cited by 2IsSuccLimit.add_natCast_ltPartialOrder · cited by 6410PartialOrderAddMonoidWithOne · cited by 313AddMonoidWithOneOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitSuccAddOrder · cited by 108SuccAddOrderIsSuccPrelimit.add_natCast_ltCITED BYCITES

Cites4

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Cited by1

Results whose statement or proof uses this declaration.