Theorems · Theorem · order theory
Int.floor_neg
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] {a : R} [IsOrderedRing R], ⌊-a⌋ = -⌈a⌉- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.floorstatement and proof · cited by 225
- Int.cast_negproof · cited by 224
- Int.ceilstatement · cited by 138
- eq_of_forall_le_iffproof · cited by 65
- Int.le_floorproof · cited by 22
- Int.ceil_leproof · cited by 17
- le_negproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Int.ceil_add_intCastproof · cited by 8
- Rat.ceil_intCast_div_natCastproof · cited by 4
- Rat.ceil_castproof · cited by 2