Theorems · Theorem · order theory
Nat.ceil_sub_natCast
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R]
[inst_4 : Sub R] [OrderedSub R] [ExistsAddOfLE R] (a : R) (n : ℕ), ⌈a - ↑n⌉₊ = ⌈a⌉₊ - n- 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.
Cites18
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
- add_zeroproof · cited by 2,707
- IsStrictOrderedRingstatement and proof · cited by 2,490
- ExistsAddOfLEstatement and proof · cited by 330
- le_totalproof · cited by 294
- OrderedSubstatement and proof · cited by 236
- FloorSemiringstatement and proof · cited by 179
- Eq.trans_leproof · cited by 155
- Nat.ceilstatement and proof · cited by 141
- tsub_add_cancel_of_leproof · cited by 112
- tsub_eq_zero_iff_leproof · cited by 32
Cited by3
Results whose statement or proof uses this declaration.
- ENat.ceil_sub_toENNRealproof · cited by 3
- Nat.ceil_sub_ofNatproof · cited by 0
- Nat.ceil_sub_oneproof · cited by 0