Theorems · Theorem · group theory
sdiv_left_cancel
∀ {G : Type u_1} {P : Type u_2} [inst : Group G] [T : Torsor G P] {p₁ p₂ p : P}, p₁ /ₛ p = p₂ /ₛ p → p₁ = p₂If dividing two points by the same point produces equal results, those points are equal.
- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- div_eq_oneproof · cited by 11
- sdiv_eq_one_iff_eqproof · cited by 3
- sdiv_div_sdiv_cancel_rightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- sdiv_left_injectiveproof · cited by 0
- sdiv_left_cancel_iffproof · cited by 0