Theorems · Theorem · group theory
sdiv_right_cancel
∀ {G : Type u_1} {P : Type u_2} [inst : Group G] [T : Torsor G P] {p₁ p₂ p : P}, p /ₛ p₁ = p /ₛ p₂ → p₁ = p₂If dividing the same point by two points produces equal results, those points are equal.
- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
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 and proof · cited by 79
- Torsorstatement and proof · cited by 65
- sdiv_smulproof · cited by 6
- smul_left_cancelproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- sdiv_right_cancel_iffproof · cited by 0
- sdiv_right_injectiveproof · cited by 0