Theorems · Theorem · number theory
round_eq_half_ceil_two_mul
∀ {α : Type u_2} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] {x : α},
2 * Int.fract x ≠ 1 → round x = ⌈2 * x⌉ / 2Away from the points with fractional part 1 / 2, round x = ⌈2 * x⌉ / 2.
- Defined in
- Mathlib.Algebra.Order.Round
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites26
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
- Set.rangeproof · cited by 4,705
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Evenproof · cited by 444
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- Oddproof · cited by 364
- two_ne_zeroproof · cited by 251
- two_mulproof · cited by 232
- Int.floorproof · cited by 225
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