Theorems · Theorem · order theory
Int.ceil_eq_iff
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] {z : ℤ} {a : R},
⌈a⌉ = z ↔ ↑z - 1 < a ∧ a ≤ ↑z- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- Int.ceilstatement and proof · cited by 138
- Int.cast_subproof · cited by 78
- le_antisymm_iffproof · cited by 62
- Int.ceil_leproof · cited by 17
- Int.lt_ceilproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Int.ceil_eq_on_Iocproof · cited by 3
- Int.fract_eq_zero_or_add_one_sub_ceilproof · cited by 2
- Int.preimage_ceil_singletonproof · cited by 1
- Irrational.beattySeq'_pos_eqproof · cited by 1
- Real.ceil_exp_one_eq_threeproof · cited by 0
- Nat.count_modEq_cardproof · cited by 0
- Real.ceil_pi_eq_fourproof · cited by 0
- NNRat.intCeil_castproof · cited by 0