Theorems · Theorem · order theory
Int.fract_div_natCast_eq_div_natCast_mod
∀ {k : Type u_4} [inst : Field k] [inst_1 : LinearOrder k] [IsOrderedRing k] [inst_3 : FloorRing k] {m n : ℕ},
Int.fract (↑m / ↑n) = ↑(m % n) / ↑n- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Fieldstatement and proof · cited by 7,404
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- IsOrderedRingstatement and proof · cited by 777
- Nat.cast_addproof · cited by 586
- mul_addproof · cited by 413
- FloorRingstatement and proof · cited by 405
- Int.cast_natCastproof · cited by 393
- div_zeroproof · cited by 251
- Nat.cast_nonneg'proof · cited by 245
- Nat.cast_pos'proof · cited by 219
Cited by3
Results whose statement or proof uses this declaration.
- abs_sub_round_div_natCast_eqproof · cited by 1
- Int.fract_div_intCast_eq_div_intCast_modproof · cited by 1
- Rat.isNNRat_intFract_of_isNNRatproof · cited by 0