Theorems · Theorem · order theory
Order.add_one_le_iff
∀ {α : Type u_1} {x y : α} [inst : Preorder α] [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α] [NoMaxOrder α],
x + 1 ≤ y ↔ x < y- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- NoMaxOrderstatement and proof · cited by 340
- SuccAddOrderstatement and proof · cited by 108
- not_isMaxproof · cited by 46
- Order.add_one_le_iff_of_not_isMaxproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Ordinal.IsFundamentalSeq.iSup_add_one_eqproof · cited by 3
- Ordinal.lt_iSup_add_oneproof · cited by 3
- Ordinal.log_opow_mul_addproof · cited by 2
- Ordinal.iSup_add_oneproof · cited by 2
- Ordinal.log_posproof · cited by 1
- Ordinal.lt_mul_iffproof · cited by 0
- Fin.sum_Iic_subproof · cited by 0
- Fin.sum_Icc_subproof · cited by 0