Theorems · Theorem · order theory
Int.ceil_eq_floor_add_one_iff_notMem
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R),
⌈a⌉ = ⌊a⌋ + 1 ↔ a ∉ Set.range Int.cast- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Set.rangestatement and proof · cited by 4,705
- le_antisymmproof · cited by 2,068
- one_ne_zeroproof · cited by 885
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- lt_of_le_of_neproof · cited by 230
- Int.floorstatement and proof · cited by 225
- Int.ceilstatement and proof · cited by 138
Cited by1
Results whose statement or proof uses this declaration.
- round_eq_half_ceil_two_mulproof · cited by 0