Theorems · Theorem · order theory
Int.ceil_eq_add_one_sub_fract
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] {a : R} [IsOrderedRing R],
Int.fract a ≠ 0 → ↑⌈a⌉ = a + 1 - Int.fract a- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites7
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
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.ceilstatement and proof · cited by 138
- Int.fractstatement and proof · cited by 114
- Int.fract_eq_zero_or_add_one_sub_ceilproof · cited by 2
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