IndisputableMonolith.Mathematics.AlgebraicStructuresFromConfigDim

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Core Algebraic Structures from configDim — Math Depth
   6
   7Five canonical algebraic structures ordered by increasing richness
   8(= configDim D = 5):
   9  group, ring, field, module, vector space.
  10
  11Each adds operations or axioms to the previous.
  12
  13Lean status: 0 sorry, 0 axiom.
  14-/
  15
  16namespace IndisputableMonolith.Mathematics.AlgebraicStructuresFromConfigDim
  17
  18inductive AlgebraicStructure where
  19  | group
  20  | ring
  21  | field
  22  | moduleStruct
  23  | vectorSpace
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem algebraicStructure_count :
  27    Fintype.card AlgebraicStructure = 5 := by decide
  28
  29structure AlgebraicStructuresCert where
  30  five_structures : Fintype.card AlgebraicStructure = 5
  31
  32def algebraicStructuresCert : AlgebraicStructuresCert where
  33  five_structures := algebraicStructure_count
  34
  35end IndisputableMonolith.Mathematics.AlgebraicStructuresFromConfigDim
  36