Theorems · Theorem · order theory
Int.ceil_intCast
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (z : ℤ), ⌈↑z⌉ = z- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 138
- eq_of_forall_ge_iffproof · cited by 96
- Int.cast_leproof · cited by 28
- Int.ceil_leproof · cited by 17
Cited by11
Results whose statement or proof uses this declaration.
- Int.ceil_oneproof · cited by 3
- BoxIntegral.unitPartition.tag_index_eq_self_of_mem_smul_spanproof · cited by 2
- Int.ceil_zeroproof · cited by 2
- tendsto_floor_left_pure_sub_oneproof · cited by 1
- tendsto_ceil_left_pureproof · cited by 1
- Int.ceil_eq_self_iff_memproof · cited by 1
- tendsto_ceil_atBotproof · cited by 0
- tendsto_ceil_atTopproof · cited by 0
- round_eq_half_ceil_two_mulproof · cited by 0
- ZSpan.ceil_eq_self_of_memproof · cited by 0
- Rat.isInt_intCeilproof · cited by 0