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Theorems · Theorem · order theory

Order.lt_add_one_iff_of_not_isMax

∀ {α : Type u_1} {x y : α} [inst : LinearOrder α] [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α],
  ¬IsMax y → (x < y + 1 ↔ x ≤ y)
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
LinearOrderAddOneSuccAddOrder
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Around this declaration

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

Order.lt_add_one_iff · cited by 13Order.lt_add_one_iffENat.lt_add_one_iff · cited by 6ENat.lt_add_one_iffLinearOrder · cited by 8572LinearOrderIsMax · cited by 372IsMaxOrder.succ_eq_add_one · cited by 115Order.succ_eq_add_oneSuccAddOrder · cited by 108SuccAddOrderOrder.lt_succ_iff_of_not_isMax · cited by 17Order.lt_succ_iff_of_not_…Order.lt_add_one_iff_of_not_i…CITED BYCITES

Cites5

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Cited by2

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