Theorems · Definition · functional analysis

WithSeminorms.recOn

{𝕜 : Type u_2} →
  {E : Type u_6} →
    {ι : Type u_9} →
      [inst : NormedField 𝕜] →
        [inst_1 : AddCommGroup E] →
          [inst_2 : Module 𝕜 E] →
            {p : SeminormFamily 𝕜 E ι} →
              [topology : TopologicalSpace E] →
                {motive : WithSeminorms p → Sort u} →
                  (t : WithSeminorms p) →
                    ((topology_eq_withSeminorms : topology = p.moduleFilterBasis.topology) → motive ⋯) → motive t

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

0 results in Mathlib

Foundations

Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpace