Theorems · Theorem · order theory
Nat.ceil_add_natCast
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R}
[IsStrictOrderedRing R], 0 ≤ a → ∀ (n : ℕ), ⌈a + ↑n⌉₊ = ⌈a⌉₊ + n- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- add_commproof · cited by 1,535
- Nat.cast_addproof · cited by 586
- le_or_gtproof · cited by 269
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement and proof · cited by 141
- eq_of_forall_ge_iffproof · cited by 96
- Nat.cast_ltproof · cited by 80
- add_lt_add_iff_rightproof · cited by 42
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- Nat.ceil_sub_natCastproof · cited by 3
- ENat.ceil_add_toENNRealproof · cited by 2
- Nat.ceil_add_oneproof · cited by 1
- Nat.ceil_add_ofNatproof · cited by 0