Theorems · Theorem · nonassociative algebras
RootPairing.range_polarizationIn_le_span_coroot
∀ {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) (S : Type u_5)
[inst_5 : CommRing S] [inst_6 : Algebra S R] [inst_7 : FaithfulSMul S R] [inst_8 : Module S M]
[inst_9 : IsScalarTower S R M] [inst_10 : Module S N] [inst_11 : P.IsValuedIn S] [inst_12 : Fintype ι],
(P.PolarizationIn S).range ≤ P.corootSpan S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- LinearMap.rangestatement and proof · cited by 893
- RootPairingstatement and proof · cited by 710
- FaithfulSMulstatement and proof · cited by 340
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.finrank_range_polarization_eq_finrank_span_corootproof · cited by 2