Theorems · Theorem · nonassociative algebras
RootPairing.invtRootSubmodule.eq_bot_iff
∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {K : Type u_5}
[inst_2 : Field K] [NeZero 2] [inst_4 : Module K M] [inst_5 : Module K N] {P : RootPairing ι K M N} [P.IsRootSystem]
(q : ↥P.invtRootSubmodule), q = ⊥ ↔ ∀ (i : ι), P.root i ∉ ↑q- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.rootstatement and proof · cited by 326
- Sublatticestatement · cited by 225
- RootPairing.IsRootSystemstatement and proof · cited by 50
- RootPairing.ne_zeroproof · cited by 32
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