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Theorems · Theorem · group theory

AddSemiconjBy.add_right

∀ {S : Type u_1} [inst : AddSemigroup S] {a x y x' y' : S},
  AddSemiconjBy a x y → AddSemiconjBy a x' y' → AddSemiconjBy a (x + x') (y + y')

If a semiconjugates x to y and x' to y', then it semiconjugates x + x' to y + y'.

Defined in
Mathlib.Algebra.Group.Semiconj.Defs
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddSemigroup
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Around this declaration

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

AddSemiconjBy.nsmul_right · cited by 5AddSemiconjBy.nsmul_rightAddCommute.add_right · cited by 4AddCommute.add_rightadd_assoc · cited by 746add_assocAddSemigroup · cited by 136AddSemigroupAddSemiconjBy · cited by 56AddSemiconjByAddSemiconjBy.eq · cited by 10AddSemiconjBy.eqAddSemiconjBy.add_rightCITED BYCITES

Cites4

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Cited by2

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