Theorems · Theorem · nonassociative algebras
RootPairing.finrank_corootSpanIn
∀ {ι : Type u_1} {M : Type u_4} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] (K : Type u_7)
{L : Type u_8} [inst_2 : Field K] [inst_3 : Field L] [inst_4 : Algebra K L] [inst_5 : Module L M]
[inst_6 : Module L N] [inst_7 : Module K M] [inst_8 : Module K N] [IsScalarTower K L M] [IsScalarTower K L N]
(Q : RootPairing ι L M N) [Q.IsRootSystem] [Q.IsValuedIn K], Module.finrank K ↥(Q.corootSpan K) = Module.finrank L N- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- Module.finrankstatement · cited by 1,770
- RootPairingstatement and proof · cited by 710
- RootPairing.IsValuedInstatement and proof · cited by 108
- RootPairing.flipproof · cited by 79
- RootPairing.IsRootSystemstatement and proof · cited by 50
- RootPairing.corootSpanstatement · cited by 31
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