Theorems · Theorem · order theory
Order.add_one_le_of_lt
∀ {α : Type u_1} {x y : α} [inst : Preorder α] [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α], x < y → x + 1 ≤ y- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PreorderAddOneSuccAddOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Order.succ_eq_add_oneproof · cited by 115
- SuccAddOrderstatement and proof · cited by 108
- Order.succ_le_of_ltproof · cited by 42
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.emultiplicity_le_one_of_separableproof · cited by 3
- emultiplicity_add_of_gtproof · cited by 3
- OrdinalApprox.lfpApprox_mem_fixedPoints_of_eqproof · cited by 3
- Ordinal.opow_mul_add_lt_opow_mulproof · cited by 2
- Order.height_add_one_leproof · cited by 1
- dvd_of_emultiplicity_posproof · cited by 1
- contDiff_tsumproof · cited by 1
- Topology.RelCWComplex.disjoint_skeleton_openCellproof · cited by 1
- SimpleGraph.two_lt_edist_iffproof · cited by 1
- Order.coheight_add_one_leproof · cited by 1
- exists_spanRank_le_and_le_height_of_le_heightproof · cited by 1