Theorems · Theorem · order theory
Int.ceil_le_floor_add_one
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] (a : R), ⌈a⌉ ≤ ⌊a⌋ + 1- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- LT.lt.leproof · cited by 2,189
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- Int.floorstatement and proof · cited by 225
- Int.ceilstatement · cited by 138
- Int.cast_addproof · cited by 124
- Int.ceil_leproof · cited by 17
- Int.lt_floor_add_oneproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Int.ceil_eq_floor_add_one_iff_notMemproof · cited by 1