Theorems · Theorem · commutative algebra
SemiconjBy.neg_left
∀ {R : Type u} [inst : Mul R] [inst_1 : HasDistribNeg R] {a x y : R}, SemiconjBy a x y → SemiconjBy (-a) x y- Defined in
- Mathlib.Algebra.Ring.Semiconj
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- MulHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- HasDistribNegstatement and proof · cited by 114
- SemiconjBystatement and proof · cited by 99
- SemiconjBy.eqproof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- Commute.neg_leftproof · cited by 3
- SemiconjBy.sub_leftproof · cited by 1
- SemiconjBy.neg_left_iffproof · cited by 1