Theorems · Theorem · field theory
Nat.cast_div_le
∀ {α : Type u_1} [inst : Semifield α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {m n : ℕ}, ↑(m / n) ≤ ↑m / ↑nNatural division is always less than division in the field.
- Defined in
- Mathlib.Data.Nat.Cast.Order.Field
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- Semifieldstatement and proof · cited by 439
- Nat.cast_mulproof · cited by 309
- div_zeroproof · cited by 251
- Nat.cast_leproof · cited by 159
- Nat.cast_posproof · cited by 113
- le_div_iff₀proof · cited by 75
Cited by4
Results whose statement or proof uses this declaration.
- Nat.roughNumbersUpTo_card_le'proof · cited by 1
- bertrand_main_inequalityproof · cited by 1
- Finpartition.IsEquipartition.card_biUnion_offDiag_le'proof · cited by 1
- EReal.natCast_div_leproof · cited by 0