finiteDimensional_inf_right — Mathlib

English

The supremum (sum) of two finite-dimensional submodules is finite-dimensional.

Русский

Супремум (сумма) двух конечномерных подпространств конечно-мерен.

LaTeX

$$$ finiteDimensional_sup\ (S_1\ S_2) : FiniteDimensional K (S_1 \ ⊔ S_2) $$$

Lean4

/-- The inf of two submodules, the second finite-dimensional, is
finite-dimensional. -/
instance finiteDimensional_inf_right (S₁ S₂ : Submodule K V) [FiniteDimensional K S₂] :
    FiniteDimensional K (S₁ ⊓ S₂ : Submodule K V) :=
  finiteDimensional_of_le inf_le_right

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