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Theorems · Theorem · order theory

Int.ceil_add_natCast

∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R) (n : ℕ),
  ⌈a + ↑n⌉ = ⌈a⌉ + ↑n
Defined in
Mathlib.Algebra.Order.Floor.Ring
Cited by
2 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Quot.sound
Assumes
RingLinearOrderFloorRingIsOrderedRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Int.ceil_add_ofNat · cited by 0Int.ceil_add_ofNatNat.count_modEq_card · cited by 0Nat.count_modEq_cardLinearOrder · cited by 8572LinearOrderRing · cited by 7463RingIsOrderedRing · cited by 777IsOrderedRingFloorRing · cited by 405FloorRingInt.cast_natCast · cited by 393Int.cast_natCastInt.ceil · cited by 138Int.ceilInt.ceil_add_intCast · cited by 8Int.ceil_add_intCastInt.ceil_add_natCastCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.