Theorems · Theorem · order theory
Int.floor_eq_iff
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] {z : ℤ} {a : R},
⌊a⌋ = z ↔ ↑z ≤ a ∧ a < ↑z + 1- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 15 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.floorstatement and proof · cited by 225
- Int.cast_addproof · cited by 124
- le_antisymm_iffproof · cited by 62
- Int.le_floorproof · cited by 22
- Int.floor_ltproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- Rat.floor_castproof · cited by 8
- Int.fract_eq_iffproof · cited by 4
- Int.floor_eq_on_Icoproof · cited by 3
- Int.image_fractproof · cited by 1
- Real.exists_rat_eq_convergent'proof · cited by 1
- Int.preimage_floor_singletonproof · cited by 1
- Int.preimage_fractproof · cited by 1
- Int.mul_fract_eq_one_iff_exists_intproof · cited by 1
- Real.floor_exp_one_eq_twoproof · cited by 0
- Real.floor_pi_eq_threeproof · cited by 0
- Real.floor_real_sqrt_eq_nat_sqrtproof · cited by 0
- Int.floor_fractproof · cited by 0