Theorems · Theorem · order theory
AddCommGroup.ModEq.toIcoMod_eq_right
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [inst_2 : IsOrderedAddMonoid α] [hα : Archimedean α]
{p : α} (hp : 0 < p) {a b : α}, a ≡ b [PMOD p] → toIocMod hp a b = a + pAlias of the forward direction of AddCommGroup.modEq_iff_toIocMod_eq_right.
- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Archimedeanstatement and proof · cited by 603
- toIocModstatement · cited by 109
- AddCommGroup.ModEqstatement · cited by 107
- AddCommGroup.modEq_iff_toIocMod_eq_rightproof · cited by 2
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