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Theorems · Theorem · ring theory

QuaternionAlgebra.im_neg

∀ {R : Type u_3} {c₁ c₂ c₃ : R} (a : QuaternionAlgebra R c₁ c₂ c₃) [inst : AddGroup R], (-a).im = -a.im
Defined in
Mathlib.Algebra.Quaternion
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
AddGroup
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Around this declaration

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

Quaternion.im_neg · cited by 0Quaternion.im_negAddGroup · cited by 4410AddGroupneg_zero · cited by 542neg_zeroQuaternionAlgebra · cited by 174QuaternionAlgebraQuaternionAlgebra.ext · cited by 21QuaternionAlgebra.extQuaternionAlgebra.im · cited by 20QuaternionAlgebra.imQuaternionAlgebra.im_negCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.