Theorems · Theorem · number theory
round_eq
∀ {α : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] (x : α),
round x = ⌊x + 1 / 2⌋- Defined in
- Mathlib.Algebra.Order.Round
- Cited by
- 8 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.
Cites14
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
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- one_divproof · cited by 624
- mul_addproof · cited by 413
- FloorRingstatement and proof · cited by 405
- Int.floorstatement and proof · cited by 225
- mul_inv_cancel₀proof · cited by 210
- Int.cast_ofNatproof · cited by 86
- two_posproof · cited by 68
- roundstatement and proof · cited by 49
- round_eq_divproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Rat.round_castproof · cited by 3
- abs_sub_roundproof · cited by 2
- round_eq_iffproof · cited by 0
- round_le_add_halfproof · cited by 0
- sub_half_lt_roundproof · cited by 0
- Int.map_roundproof · cited by 0
- Real.round_exp_one_eq_threeproof · cited by 0
- Real.round_pi_eq_threeproof · cited by 0