Theorems · Theorem · number theory

Module.Basis.ofZLatticeBasis_comap

∀ (K : Type u_1) [inst : NormedField K] [inst_1 : LinearOrder K] [inst_2 : IsStrictOrderedRing K]
  [inst_3 : HasSolidNorm K] [inst_4 : FloorRing K] {E : Type u_2} [inst_5 : NormedAddCommGroup E]
  [inst_6 : NormedSpace K E] [inst_7 : FiniteDimensional K E] [inst_8 : ProperSpace E] {F : Type u_3}
  [inst_9 : NormedAddCommGroup F] [inst_10 : NormedSpace K F] [inst_11 : FiniteDimensional K F]
  [inst_12 : ProperSpace F] (L : Submodule ℤ E) [inst_13 : DiscreteTopology ↥L] [inst_14 : IsZLattice K L]
  (e : F ≃L[K] E) {ι : Type u_4} (b : Module.Basis ι ℤ ↥L),
  Module.Basis.ofZLatticeBasis K (ZLattice.comap K L ↑↑e) (Module.Basis.ofZLatticeComap K L (↑e) b) =
    (Module.Basis.ofZLatticeBasis K L b).map ↑e.symm

Defined in

Mathlib.Algebra.Module.ZLattice.Basic

Cited by

1 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldLinearOrderIsStrictOrderedRingHasSolidNormFloorRingNormedAddCommGroupNormedSpaceFiniteDimensionalProperSpaceNormedAddCommGroupNormedSpaceFiniteDimensionalProperSpaceDiscreteTopologyIsZLattice