Theorems · Theorem · group theory
inv_sdiv_eq_sdiv_rev
∀ {G : Type u_1} {P : Type u_2} [inst : Group G] [T : Torsor G P] (p₁ p₂ : P), (p₁ /ₛ p₂)⁻¹ = p₂ /ₛ p₁Dividing two points in the reverse order produces the inverse of dividing them.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- inv_eq_of_mul_eq_one_rightproof · cited by 15
- sdiv_selfproof · cited by 6
- smul_right_cancelproof · cited by 5
- sdiv_mul_sdiv_cancelproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- sdiv_smul_eq_sdiv_divproof · cited by 6
- sdiv_div_sdiv_cancel_leftproof · cited by 1
- smul_sdiv_eq_div_sdivproof · cited by 0