Theorems · Theorem · order theory
Int.ceil_eq_self_iff_mem
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R),
↑⌈a⌉ = a ↔ a ∈ Set.range Int.cast- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 4,705
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.ceilstatement and proof · cited by 138
- Int.ceil_intCastproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Int.ceil_eq_floor_add_one_iff_notMemproof · cited by 1