Theorems · Theorem · linear algebra
LinearMap.toPerfPair_apply
∀ {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) [inst_5 : p.IsPerfPair] (x : M) (y : N),
(p.toPerfPair x) y = (p x) y- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- LinearEquivstatement · cited by 3,317
- Module.Dualstatement · cited by 583
- LinearMap.toPerfPairstatement · cited by 46
- LinearMap.IsPerfPairstatement and proof · cited by 34
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