Theorems · Theorem · nonassociative algebras

RootPairing.EmbeddedG2.allRoots_subset_range_root

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N)
  [inst_5 : P.EmbeddedG2] [inst_6 : DecidableEq M], ↑(RootPairing.EmbeddedG2.allRoots P).toFinset ⊆ Set.range ⇑P.root

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.G2
Cited by: 0 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module RootPairing.EmbeddedG2 DecidableEq

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DFunLike.coestatement · cited by 62,936
Setstatement and proof · cited by 53,352
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
Finsetstatement · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
SetLike.coestatement and proof · cited by 8,199
Set.rangestatement · cited by 4,705
Function.Embeddingstatement · cited by 988
RootPairingstatement and proof · cited by 710
RootPairing.rootstatement and proof · cited by 326
Finset.coe_singletonproof · cited by 145

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