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Theorems · Theorem · ring theory

QuaternionAlgebra.re_add_im

∀ {R : Type u_3} {c₁ c₂ c₃ : R} (a : QuaternionAlgebra R c₁ c₂ c₃) [inst : AddGroup R], ↑a.re + a.im = a
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.re_add_im · cited by 1Quaternion.re_add_imAddGroup · cited by 4410AddGroupadd_zero · cited by 2707add_zerozero_add · cited by 2366zero_addQuaternionAlgebra · cited by 174QuaternionAlgebraQuaternionAlgebra.re · cited by 117QuaternionAlgebra.reQuaternionAlgebra.imI · cited by 91QuaternionAlgebra.imIQuaternionAlgebra.imJ · cited by 80QuaternionAlgebra.imJQuaternionAlgebra.imK · cited by 78QuaternionAlgebra.imKQuaternionAlgebra.coe · cited by 46QuaternionAlgebra.coeQuaternionAlgebra.ext · cited by 21QuaternionAlgebra.extQuaternionAlgebra.im · cited by 20QuaternionAlgebra.imQuaternionAlgebra.re_add_imCITED BYCITES

Cites11

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Cited by1

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