IndisputableMonolith.Mathematics.ElementaryRegularNumberSystems

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Elementary Regular Number Systems — Math Structural Depth
   6
   7Five canonical number system tiers (= configDim D = 5):
   8  ℕ (naturals), ℤ (integers), ℚ (rationals), ℝ (reals), ℂ (complexes).
   9
  10Each tier adds one canonical algebraic closure step. Standard and
  11well-known structurally.
  12
  13Lean status: 0 sorry, 0 axiom.
  14-/
  15
  16namespace IndisputableMonolith.Mathematics.ElementaryRegularNumberSystems
  17
  18inductive NumberSystem where
  19  | naturals
  20  | integers
  21  | rationals
  22  | reals
  23  | complexes
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem numberSystem_count : Fintype.card NumberSystem = 5 := by decide
  27
  28structure NumberSystemCert where
  29  five_systems : Fintype.card NumberSystem = 5
  30
  31def numberSystemCert : NumberSystemCert where
  32  five_systems := numberSystem_count
  33
  34end IndisputableMonolith.Mathematics.ElementaryRegularNumberSystems
  35