Theorems · Theorem · group theory
sdiv_eq_one_iff_eq
∀ {G : Type u_1} {P : Type u_2} [inst : Group G] [T : Torsor G P] {p₁ p₂ : P}, p₁ /ₛ p₂ = 1 ↔ p₁ = p₂Dividing two points produces 1 if and only if they are equal.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
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.
- Groupstatement and proof · cited by 6,238
- SDiv.sdivstatement · cited by 79
- Torsorstatement and proof · cited by 65
- sdiv_selfproof · cited by 6
- eq_of_sdiv_eq_oneproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- sdiv_left_cancelproof · cited by 2
- sdiv_smul_commproof · cited by 1
- sdiv_ne_oneproof · cited by 0