Theorems · Definition · group theory
unitsEquivNeZero
{G₀ : Type u_1} → [inst : GroupWithZero G₀] → G₀ˣ ≃ { a // a ≠ 0 }In a GroupWithZero G₀, the unit group G₀ˣ is equivalent to the subtype of nonzero
elements.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- GroupWithZerostatement and proof · cited by 691
- Units.mk0proof · cited by 181
Cited by3
Results whose statement or proof uses this declaration.
- Nat.card_unitsproof · cited by 6
- unitsEquivNeZero_apply_coestatement and proof · cited by 0
- unitsEquivNeZero_symm_applystatement and proof · cited by 0