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Theorems · Theorem · order theory

Order.IsSuccPrelimit.add_one_lt

∀ {α : Type u_1} {x y : α} [inst : PartialOrder α] [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α],
  Order.IsSuccPrelimit x → y < x → y + 1 < x
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderAddOneSuccAddOrder
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Around this declaration

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

Order.IsSuccLimit.add_one_lt · cited by 2IsSuccLimit.add_one_ltCardinal.isStrongPrelimit_preBeth · cited by 1Cardinal.isStrongPrelimit…PartialOrder · cited by 6410PartialOrderOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitOrder.succ_eq_add_one · cited by 115Order.succ_eq_add_oneSuccAddOrder · cited by 108SuccAddOrderOrder.IsSuccPrelimit.succ_lt · cited by 7IsSuccPrelimit.succ_ltIsSuccPrelimit.add_one_ltCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.