Theorems · Theorem · order theory
Nat.floor_of_nonpos
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R}
[IsStrictOrderedRing R], a ≤ 0 → ⌊a⌋₊ = 0- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 40 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.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- LE.le.lt_or_eqproof · cited by 48
- Nat.floor_zeroproof · cited by 6
- FloorSemiring.floor_of_negproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Nat.floor_monoproof · cited by 8
- Nat.le_floor_iff'proof · cited by 7
- Nat.floor_sub_natCastproof · cited by 3
- Nat.mul_cast_floor_div_cancelproof · cited by 2
- Nat.pos_of_floor_posproof · cited by 2
- Nat.floor_lt_ceil_of_lt_of_posproof · cited by 1
- Nat.floor_congrproof · cited by 1
- Nat.floor_le_ceilproof · cited by 0
- Mathlib.Meta.NormNum.IsInt.natFloorproof · cited by 0