Theorems · Theorem · order theory
Int.ceil_add_intCast
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R) (z : ℤ),
⌈a + ↑z⌉ = ⌈a⌉ + z- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.floorproof · cited by 225
- Int.ceilstatement and proof · cited by 138
- neg_injproof · cited by 85
- neg_add'proof · cited by 20
- Int.floor_negproof · cited by 3
- Int.floor_sub_intCastproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Int.ceil_lt_add_oneproof · cited by 7
- round_add_intCastproof · cited by 4
- Int.ceil_add_natCastproof · cited by 2
- Int.ceil_intCast_addproof · cited by 2
- Int.ceil_add_oneproof · cited by 1
- Int.ceil_sub_intCastproof · cited by 1
- CircleDeg1Lift.ceil_map_map_zero_leproof · cited by 0
- CircleDeg1Lift.le_ceil_map_map_zeroproof · cited by 0