Theorems · Theorem · nonassociative algebras
RootPairing.isAnisotropic_of_isValuedIn
∀ {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 : Module R M] [inst_5 : Module R N] (P : RootPairing ι R M N)
(S : Type u_5) [inst_6 : CommRing S] [inst_7 : LinearOrder S] [IsStrictOrderedRing S] [inst_9 : Algebra S R]
[FaithfulSMul S R] [P.IsValuedIn S], P.IsAnisotropic- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- IsStrictOrderedRingstatement and proof · cited by 2,490
- RootPairingstatement and proof · cited by 710
- FaithfulSMulstatement and proof · cited by 340
- RootPairing.IsValuedInstatement and proof · cited by 108
- RootPairing.flipproof · cited by 79
- RootPairing.IsAnisotropicstatement · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.posRootForm_posForm_pos_of_ne_zeroproof · cited by 3