Theorems · Theorem · nonassociative algebras
RootPairing.eq_zero_of_mem_rootSpan_of_rootForm_self_eq_zero
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup N] [inst_3 : CommRing R] [inst_4 : LinearOrder R] [IsStrictOrderedRing R] [inst_6 : Module R M]
[inst_7 : Module R N] (P : RootPairing ι R M N) {x : M}, x ∈ P.rootSpan R → (P.RootForm x) x = 0 → x = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LinearMap.kerproof · cited by 848
- RootPairingstatement and proof · cited by 710
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.rootForm_anisotropicproof · cited by 0
- RootPairing.rootForm_pos_of_ne_zeroproof · cited by 0