Theorems · Theorem · order theory
Nat.ceil_zero
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R],
⌈0⌉₊ = 0- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Nat.cast_zeroproof · cited by 1,870
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement and proof · cited by 141
- Nat.ceil_natCastproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Int.log_natCastproof · cited by 3
- NNRat.ceil_castproof · cited by 1
- Real.natCeil_logb_natCastproof · cited by 0