Theorems · Theorem · group theory
DivisibleHull.qsmul_of_nonpos
∀ {M : Type u_2} [inst : AddCommGroup M] {a : ℚ} (h : a ≤ 0) (x : DivisibleHull M),
a • x =
-((have this := ⟨-a, ⋯⟩;
this) •
x)- Defined in
- Mathlib.GroupTheory.DivisibleHull
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- absproof · cited by 1,814
- one_smulproof · cited by 1,374
- nonZeroDivisorsstatement · cited by 895
- zero_smulproof · cited by 716
- smul_zeroproof · cited by 665
- neg_zeroproof · cited by 542
- NNRatstatement and proof · cited by 523
- neg_smulproof · cited by 306
- LE.le.eq_or_ltproof · cited by 220
- abs_nonnegproof · cited by 168
- abs_zeroproof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- DivisibleHull.qsmul_mkproof · cited by 1