Mathlib Map

Theorems · Theorem · group theory

SemiconjBy.eq

∀ {S : Type u_1} [inst : Mul S] {a x y : S}, SemiconjBy a x y → a * x = y * a

Equality behind SemiconjBy a x y; useful for rewriting.

Defined in
Mathlib.Algebra.Group.Semiconj.Defs
Cited by
18 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SemiconjBy.mul_left · cited by 5SemiconjBy.mul_leftSemiconjBy.mul_right · cited by 5SemiconjBy.mul_rightSemiconjBy.neg_left · cited by 3SemiconjBy.neg_leftSemiconjBy.neg_right · cited by 3SemiconjBy.neg_rightSemiconjBy.smul_right · cited by 3SemiconjBy.smul_rightSemiconjBy.units_inv_right · cited by 3SemiconjBy.units_inv_rightSemiconjBy.units_inv_symm_left · cited by 3SemiconjBy.units_inv_symm…MonoidHom.map_isConj · cited by 2MonoidHom.map_isConjSemiconjBy.add_right · cited by 2SemiconjBy.add_rightSemiconjBy.smul_left · cited by 2SemiconjBy.smul_leftSemiconjBy.star_right · cited by 2SemiconjBy.star_rightSemiconjBy.add_left · cited by 2SemiconjBy.add_leftSemiconjBy.eq_one_iff · cited by 1SemiconjBy.eq_one_iffSemiconjBy.function_semiconj_mul_left · cited by 1SemiconjBy.function_semic…SemiconjBy.function_semiconj_mul_right_swap · cited by 1SemiconjBy.function_semic…SemiconjBy · cited by 99SemiconjBySemiconjBy.eqCITED BYCITES

Cites1

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.