Theorems · Theorem · order theory
Int.fract_eq_zero_or_add_one_sub_ceil
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R),
Int.fract a = 0 ∨ Int.fract a = a + 1 - ↑⌈a⌉- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- le_of_ltproof · cited by 1,175
- eq_or_neproof · cited by 1,117
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- Int.floorproof · cited by 225
- add_tsub_cancel_rightproof · cited by 172
- Int.ceilstatement and proof · cited by 138
- Int.cast_addproof · cited by 124
- Int.fractstatement and proof · cited by 114
Cited by2
Results whose statement or proof uses this declaration.
- Int.ceil_sub_self_eqproof · cited by 1
- Int.ceil_eq_add_one_sub_fractproof · cited by 0