Theorems · Theorem · number theory
ZMod.lift_injective
∀ (n : ℕ) {A : Type u_2} [inst : AddGroup A] {f : { f // f ↑n = 0 }},
Function.Injective ⇑((ZMod.lift n) f) ↔ ∀ (m : ℤ), ↑f m = 0 → ↑m = 0- Defined in
- Mathlib.Data.ZMod.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Equivstatement · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement and proof · cited by 3,230
- ZModstatement and proof · cited by 1,024
- Function.Surjective.forallproof · cited by 214
- ZMod.intCast_surjectiveproof · cited by 8
- ZMod.liftstatement and proof · cited by 5
- ZMod.lift_coeproof · cited by 3
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