IndisputableMonolith.Mathematics.LogicSystemsFromConfigDim

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Mathematical Logic Systems from configDim — Math Depth
   6
   7Five canonical logic systems (= configDim D = 5):
   8  propositional, first-order, second-order, modal, intuitionistic.
   9
  10Lean status: 0 sorry, 0 axiom.
  11-/
  12
  13namespace IndisputableMonolith.Mathematics.LogicSystemsFromConfigDim
  14
  15inductive LogicSystem where
  16  | propositional
  17  | firstOrder
  18  | secondOrder
  19  | modal
  20  | intuitionistic
  21  deriving DecidableEq, Repr, BEq, Fintype
  22
  23theorem logicSystem_count : Fintype.card LogicSystem = 5 := by decide
  24
  25structure LogicSystemsCert where
  26  five_systems : Fintype.card LogicSystem = 5
  27
  28def logicSystemsCert : LogicSystemsCert where
  29  five_systems := logicSystem_count
  30
  31end IndisputableMonolith.Mathematics.LogicSystemsFromConfigDim
  32