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Theorems · Theorem · ring theory

AddOpposite.op_inj

∀ {α : Type u_1} {x y : α}, AddOpposite.op x = AddOpposite.op y ↔ x = y
Defined in
Mathlib.Algebra.Opposites
Cited by
5 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext
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Around this declaration

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

UniqueAdd.of_addOpposite · cited by 4UniqueAdd.of_addOppositeAddOpposite.addSemiconjBy_op · cited by 3AddOpposite.addSemiconjBy…AddOpposite.op_mem_center_iff · cited by 1AddOpposite.op_mem_center…AddOpposite.isDedekindFiniteAddMonoid_iff · cited by 0AddOpposite.isDedekindFin…AddUnits.isOpenMap_map · cited by 0AddUnits.isOpenMap_mapAddOpposite · cited by 452AddOppositeAddOpposite.op · cited by 192AddOpposite.opPreOpposite.op'.injEq · cited by 2op'.injEqAddOpposite.op_injCITED BYCITES

Cites3

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

Cited by5

Results whose statement or proof uses this declaration.