Theorems · Theorem · group theory
sdiv_smul
∀ {G : Type u_1} {P : Type u_2} [inst : Group G] [T : Torsor G P] (p₁ p₂ : P), (p₁ /ₛ p₂) • p₂ = p₁Scalar multiplying the result of dividing another point produces that point.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Torsor.sdiv_smul'proof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- smul_sdiv_assocproof · cited by 7
- sdiv_mul_sdiv_cancelproof · cited by 4
- Equiv.smulConstproof · cited by 3
- sdiv_right_cancelproof · cited by 2
- eq_smul_iff_sdiv_eqproof · cited by 1
- eq_of_sdiv_eq_oneproof · cited by 1
- sdiv_div_sdiv_cancel_rightproof · cited by 1