Theorems · Theorem · order theory
toIocDiv_mul_sub_toIocMod
∀ {R : Type u_1} [inst : NonAssocRing R] [inst_1 : LinearOrder R] [inst_2 : IsOrderedAddMonoid R]
[inst_3 : Archimedean R] {p : R} (hp : 0 < p) (a b : R), ↑(toIocDiv hp a b) * p + toIocMod hp a b = b- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- add_commproof · cited by 1,535
- Archimedeanstatement and proof · cited by 603
- NonAssocRingstatement and proof · cited by 483
- toIocModstatement and proof · cited by 109
- toIocDivstatement and proof · cited by 85
- toIocMod_add_toIocDiv_mulproof · cited by 1
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