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Theorems · Theorem · ring theory

QuaternionAlgebra.coe_neg

∀ {R : Type u_3} {c₁ c₂ c₃ : R} (x : R) [inst : AddGroup R], ↑(-x) = -↑x
Defined in
Mathlib.Algebra.Quaternion
Cited by
2 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.

QuaternionAlgebra.star_mul_eq_coe · cited by 2QuaternionAlgebra.star_mu…Quaternion.coe_neg · cited by 2Quaternion.coe_negAddGroup · cited by 4410AddGroupneg_zero · cited by 542neg_zeroQuaternionAlgebra · cited by 174QuaternionAlgebraQuaternionAlgebra.coe · cited by 46QuaternionAlgebra.coeQuaternionAlgebra.ext · cited by 21QuaternionAlgebra.extQuaternionAlgebra.coe_negCITED BYCITES

Cites5

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

Cited by2

Results whose statement or proof uses this declaration.