Theorems · Theorem · group theory
smul_sdiv
∀ {G : Type u_1} {P : Type u_2} [inst : Group G] [T : Torsor G P] (g : G) (p : P), g • p /ₛ p = gMultiplying by a group element then dividing by the original point produces that group element.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 4 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.smul_sdiv'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- sdiv_selfproof · cited by 6
- sdiv_smul_eq_sdiv_divproof · cited by 6
- smul_right_cancelproof · cited by 5
- Equiv.smulConstproof · cited by 3
- eq_smul_iff_sdiv_eqproof · cited by 1