Theorems · Theorem · linear algebra
Module.IsReflexive.of_isPerfPair
∀ {R : Type u_1} {M : Type u_3} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] [inst_2 : CommRing R]
[inst_3 : Module R M] [inst_4 : Module R N] (p : M →ₗ[R] N →ₗ[R] R) [p.IsPerfPair], Module.IsReflexive R M- Cited by
- 29 results in Mathlib
- Foundations
- Depth 42 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 and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- LinearEquiv.symmproof · cited by 1,461
- Function.Bijectiveproof · cited by 863
- LinearMap.extproof · cited by 844
- Module.Dualproof · cited by 583
- LinearEquiv.transproof · cited by 298
- LinearMap.flipproof · cited by 193
Cited by29
Results whose statement or proof uses this declaration.
- RootPairing.root_sub_root_mem_of_pairingIn_posproof · cited by 7
- RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRedproof · cited by 6
- RootPairing.disjoint_rootSpan_ker_rootFormproof · cited by 5
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- RootPairing.isCompl_rootSpan_ker_rootFormproof · cited by 4
- RootPairing.pairing_eq_zero_iff'proof · cited by 3
- RootPairing.linearIndependent_of_add_mem_range_root'proof · cited by 3
- RootPairing.Base.root_sub_root_mem_of_mem_of_memproof · cited by 3
- RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed'proof · cited by 2
- RootPairing.EmbeddedG2.isOrthogonal_short_and_longproof · cited by 2
- RootPairing.finrank_range_polarization_eq_finrank_span_corootproof · cited by 2
- RootPairing.ne_negproof · cited by 2