Pell Light All Matching Certificates 001

import Init
import Mathlib.Data.List.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_PellLightMatchingBridge_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField103_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField119_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField127_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField23_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField31_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField47_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField71_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField79_Definitions
import Definitions.Def_D1Bound5_PellLightMatchingField7_Definitions_RecoverySplit20261024
import Definitions.Def_D1Bound5_PellLightMatchingPilot_Definitions
import Definitions.Def_D1Bound5_PellLightMatching_Definitions
import Definitions.Def_D1Bound5_PellMatchingCheck_Definitions

section
namespace D1Bound5
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000

def pellMagnitudes_4519 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_4519

def pellMasks_4519 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_4519.map pellLightMasksToOriginal

def pellWitnesses_4519 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_4519

theorem pellMasks_4519_valid : ∀ m ∈ pellMasks_4519, m.Valid 4519 := by
  exact pellLightMasks_valid 4519 PellMatchingLightProduction.pellMasks_4519 PellMatchingLightProduction.pellMasks_4519_valid

theorem pellMatching_4519_checked :
    pellMatchingCheck pellMasks_4519 pellMagnitudes_4519 pellWitnesses_4519 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_4519
    PellMatchingLightProduction.pellMagnitudes_4519 PellMatchingLightProduction.pellWitnesses_4519).symm.trans
      PellMatchingLightProduction.pellMatching_4519_checked

theorem pellMagnitudes_4519_large : ∀ x ∈ pellMagnitudes_4519, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_4519 PellMatchingLightProduction.pellMagnitudes_4519_large

def pellGraphCertificate_4519 : PellMatchingCertificate 4519 where
  magnitudes := pellMagnitudes_4519
  masks := pellMasks_4519
  witnesses := pellWitnesses_4519
  masks_valid := pellMasks_4519_valid
  checked := pellMatching_4519_checked
  large := pellMagnitudes_4519_large

def pellMagnitudes_7 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_7

def pellMasks_7 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_7.map pellLightMasksToOriginal

def pellWitnesses_7 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_7

theorem pellMasks_7_valid : ∀ m ∈ pellMasks_7, m.Valid 7 := by
  exact pellLightMasks_valid 7 PellMatchingLightProduction.pellMasks_7 PellMatchingLightProduction.pellMasks_7_valid

theorem pellMatching_7_checked :
    pellMatchingCheck pellMasks_7 pellMagnitudes_7 pellWitnesses_7 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_7
    PellMatchingLightProduction.pellMagnitudes_7 PellMatchingLightProduction.pellWitnesses_7).symm.trans
      PellMatchingLightProduction.pellMatching_7_checked

theorem pellMagnitudes_7_large : ∀ x ∈ pellMagnitudes_7, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_7 PellMatchingLightProduction.pellMagnitudes_7_large

def pellGraphCertificate_7 : PellMatchingCertificate 7 where
  magnitudes := pellMagnitudes_7
  masks := pellMasks_7
  witnesses := pellWitnesses_7
  masks_valid := pellMasks_7_valid
  checked := pellMatching_7_checked
  large := pellMagnitudes_7_large

def pellMagnitudes_23 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_23

def pellMasks_23 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_23.map pellLightMasksToOriginal

def pellWitnesses_23 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_23

theorem pellMasks_23_valid : ∀ m ∈ pellMasks_23, m.Valid 23 := by
  exact pellLightMasks_valid 23 PellMatchingLightProduction.pellMasks_23 PellMatchingLightProduction.pellMasks_23_valid

theorem pellMatching_23_checked :
    pellMatchingCheck pellMasks_23 pellMagnitudes_23 pellWitnesses_23 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_23
    PellMatchingLightProduction.pellMagnitudes_23 PellMatchingLightProduction.pellWitnesses_23).symm.trans
      PellMatchingLightProduction.pellMatching_23_checked

theorem pellMagnitudes_23_large : ∀ x ∈ pellMagnitudes_23, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_23 PellMatchingLightProduction.pellMagnitudes_23_large

def pellGraphCertificate_23 : PellMatchingCertificate 23 where
  magnitudes := pellMagnitudes_23
  masks := pellMasks_23
  witnesses := pellWitnesses_23
  masks_valid := pellMasks_23_valid
  checked := pellMatching_23_checked
  large := pellMagnitudes_23_large

def pellMagnitudes_31 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_31

def pellMasks_31 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_31.map pellLightMasksToOriginal

def pellWitnesses_31 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_31

theorem pellMasks_31_valid : ∀ m ∈ pellMasks_31, m.Valid 31 := by
  exact pellLightMasks_valid 31 PellMatchingLightProduction.pellMasks_31 PellMatchingLightProduction.pellMasks_31_valid

theorem pellMatching_31_checked :
    pellMatchingCheck pellMasks_31 pellMagnitudes_31 pellWitnesses_31 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_31
    PellMatchingLightProduction.pellMagnitudes_31 PellMatchingLightProduction.pellWitnesses_31).symm.trans
      PellMatchingLightProduction.pellMatching_31_checked

theorem pellMagnitudes_31_large : ∀ x ∈ pellMagnitudes_31, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_31 PellMatchingLightProduction.pellMagnitudes_31_large

def pellGraphCertificate_31 : PellMatchingCertificate 31 where
  magnitudes := pellMagnitudes_31
  masks := pellMasks_31
  witnesses := pellWitnesses_31
  masks_valid := pellMasks_31_valid
  checked := pellMatching_31_checked
  large := pellMagnitudes_31_large

def pellMagnitudes_47 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_47

def pellMasks_47 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_47.map pellLightMasksToOriginal

def pellWitnesses_47 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_47

theorem pellMasks_47_valid : ∀ m ∈ pellMasks_47, m.Valid 47 := by
  exact pellLightMasks_valid 47 PellMatchingLightProduction.pellMasks_47 PellMatchingLightProduction.pellMasks_47_valid

theorem pellMatching_47_checked :
    pellMatchingCheck pellMasks_47 pellMagnitudes_47 pellWitnesses_47 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_47
    PellMatchingLightProduction.pellMagnitudes_47 PellMatchingLightProduction.pellWitnesses_47).symm.trans
      PellMatchingLightProduction.pellMatching_47_checked

theorem pellMagnitudes_47_large : ∀ x ∈ pellMagnitudes_47, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_47 PellMatchingLightProduction.pellMagnitudes_47_large

def pellGraphCertificate_47 : PellMatchingCertificate 47 where
  magnitudes := pellMagnitudes_47
  masks := pellMasks_47
  witnesses := pellWitnesses_47
  masks_valid := pellMasks_47_valid
  checked := pellMatching_47_checked
  large := pellMagnitudes_47_large

def pellMagnitudes_71 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_71

def pellMasks_71 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_71.map pellLightMasksToOriginal

def pellWitnesses_71 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_71

theorem pellMasks_71_valid : ∀ m ∈ pellMasks_71, m.Valid 71 := by
  exact pellLightMasks_valid 71 PellMatchingLightProduction.pellMasks_71 PellMatchingLightProduction.pellMasks_71_valid

theorem pellMatching_71_checked :
    pellMatchingCheck pellMasks_71 pellMagnitudes_71 pellWitnesses_71 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_71
    PellMatchingLightProduction.pellMagnitudes_71 PellMatchingLightProduction.pellWitnesses_71).symm.trans
      PellMatchingLightProduction.pellMatching_71_checked

theorem pellMagnitudes_71_large : ∀ x ∈ pellMagnitudes_71, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_71 PellMatchingLightProduction.pellMagnitudes_71_large

def pellGraphCertificate_71 : PellMatchingCertificate 71 where
  magnitudes := pellMagnitudes_71
  masks := pellMasks_71
  witnesses := pellWitnesses_71
  masks_valid := pellMasks_71_valid
  checked := pellMatching_71_checked
  large := pellMagnitudes_71_large

def pellMagnitudes_79 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_79

def pellMasks_79 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_79.map pellLightMasksToOriginal

def pellWitnesses_79 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_79

theorem pellMasks_79_valid : ∀ m ∈ pellMasks_79, m.Valid 79 := by
  exact pellLightMasks_valid 79 PellMatchingLightProduction.pellMasks_79 PellMatchingLightProduction.pellMasks_79_valid

theorem pellMatching_79_checked :
    pellMatchingCheck pellMasks_79 pellMagnitudes_79 pellWitnesses_79 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_79
    PellMatchingLightProduction.pellMagnitudes_79 PellMatchingLightProduction.pellWitnesses_79).symm.trans
      PellMatchingLightProduction.pellMatching_79_checked

theorem pellMagnitudes_79_large : ∀ x ∈ pellMagnitudes_79, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_79 PellMatchingLightProduction.pellMagnitudes_79_large

def pellGraphCertificate_79 : PellMatchingCertificate 79 where
  magnitudes := pellMagnitudes_79
  masks := pellMasks_79
  witnesses := pellWitnesses_79
  masks_valid := pellMasks_79_valid
  checked := pellMatching_79_checked
  large := pellMagnitudes_79_large

def pellMagnitudes_103 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_103

def pellMasks_103 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_103.map pellLightMasksToOriginal

def pellWitnesses_103 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_103

theorem pellMasks_103_valid : ∀ m ∈ pellMasks_103, m.Valid 103 := by
  exact pellLightMasks_valid 103 PellMatchingLightProduction.pellMasks_103 PellMatchingLightProduction.pellMasks_103_valid

theorem pellMatching_103_checked :
    pellMatchingCheck pellMasks_103 pellMagnitudes_103 pellWitnesses_103 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_103
    PellMatchingLightProduction.pellMagnitudes_103 PellMatchingLightProduction.pellWitnesses_103).symm.trans
      PellMatchingLightProduction.pellMatching_103_checked

theorem pellMagnitudes_103_large : ∀ x ∈ pellMagnitudes_103, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_103 PellMatchingLightProduction.pellMagnitudes_103_large

def pellGraphCertificate_103 : PellMatchingCertificate 103 where
  magnitudes := pellMagnitudes_103
  masks := pellMasks_103
  witnesses := pellWitnesses_103
  masks_valid := pellMasks_103_valid
  checked := pellMatching_103_checked
  large := pellMagnitudes_103_large

def pellMagnitudes_119 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_119

def pellMasks_119 : List PellSquareMasks :=
  PellMatchingLightProduction.pellMasks_119.map pellLightMasksToOriginal

def pellWitnesses_119 : List (List (ℕ × ℕ)) :=
  PellMatchingLightProduction.pellWitnesses_119

theorem pellMasks_119_valid : ∀ m ∈ pellMasks_119, m.Valid 119 := by
  exact pellLightMasks_valid 119 PellMatchingLightProduction.pellMasks_119 PellMatchingLightProduction.pellMasks_119_valid

theorem pellMatching_119_checked :
    pellMatchingCheck pellMasks_119 pellMagnitudes_119 pellWitnesses_119 = true := by
  exact (pellLightMatchingCheck_eq PellMatchingLightProduction.pellMasks_119
    PellMatchingLightProduction.pellMagnitudes_119 PellMatchingLightProduction.pellWitnesses_119).symm.trans
      PellMatchingLightProduction.pellMatching_119_checked

theorem pellMagnitudes_119_large : ∀ x ∈ pellMagnitudes_119, 2 ≤ x := by
  exact pellLightMagnitudes_large PellMatchingLightProduction.pellMagnitudes_119 PellMatchingLightProduction.pellMagnitudes_119_large

def pellGraphCertificate_119 : PellMatchingCertificate 119 where
  magnitudes := pellMagnitudes_119
  masks := pellMasks_119
  witnesses := pellWitnesses_119
  masks_valid := pellMasks_119_valid
  checked := pellMatching_119_checked
  large := pellMagnitudes_119_large

def pellMagnitudes_127 : List ℤ :=
  PellMatchingLightProduction.pellMagnitudes_127































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































end D1Bound5
end