Theorems · Theorem · order theory
Int.floor_add_fract
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] (a : R), ↑⌊a⌋ + Int.fract a = a- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.floorstatement and proof · cited by 225
- add_sub_cancelproof · cited by 195
- Int.fractstatement · cited by 114
Cited by4
Results whose statement or proof uses this declaration.
- round_eq_divproof · cited by 2
- GenContFract.compExactValue_correctness_of_stream_eq_someproof · cited by 2
- Rat.num_lt_succ_floor_mul_denproof · cited by 1
- Int.fract_negproof · cited by 0