Theorems · Theorem · linear algebra

Module.finrank_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.Finite R M]
  [Module.Free R M], Module.finrank R M = Module.finrank R N

Defined in: Mathlib.LinearAlgebra.PerfectPairing.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup AddCommGroup CommRing Module Module LinearMap.IsPerfPair Module.Finite Module.Free

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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
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
Module.finrankstatement · cited by 1,770
LinearEquiv.symmproof · cited by 1,461
Module.Finitestatement and proof · cited by 1,032
Module.Freestatement and proof · cited by 597
LinearEquiv.transproof · cited by 298
LinearMap.flipproof · cited by 193
Module.Free.chooseBasisproof · cited by 121

Cited by1

Results whose statement or proof uses this declaration.

LinearMap.exists_basis_basis_of_span_eq_top_of_mem_algebraMapproof · cited by 1