Theorems · Definition · order theory

HahnEmbedding.Partial.extendFun

{K : Type u_1} →
  [inst : DivisionRing K] →
    [inst_1 : LinearOrder K] →
      [inst_2 : IsOrderedRing K] →
        [inst_3 : Archimedean K] →
          {M : Type u_2} →
            [inst_4 : AddCommGroup M] →
              [inst_5 : LinearOrder M] →
                [inst_6 : IsOrderedAddMonoid M] →
                  [inst_7 : Module K M] →
                    [inst_8 : IsOrderedModule K M] →
                      {R : Type u_3} →
                        [inst_9 : AddCommGroup R] →
                          [inst_10 : LinearOrder R] →
                            [inst_11 : Module K R] →
                              {seed : HahnEmbedding.Seed K M R} →
                                (f : HahnEmbedding.Partial seed) →
                                  [IsOrderedAddMonoid R] →
                                    [Archimedean R] →
                                      {x : M} → x ∉ (↑f).domain → M →ₗ.[K] Lex (HahnSeries (FiniteArchimedeanClass M) R)

Extend f to a larger partial linear map by adding a new x.

Defined in

Mathlib.Algebra.Order.Module.HahnEmbedding

Cited by

5 results in Mathlib

Foundations

Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingLinearOrderIsOrderedRingArchimedeanAddCommGroupLinearOrderIsOrderedAddMonoidModuleIsOrderedModuleAddCommGroupLinearOrderModuleIsOrderedAddMonoidArchimedean