OAI/NumberTheory/Ostmann/Arithmetic/ReconstructionIntegrality.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

1. def OAI.Ostmann.HistoryFormula.IntegralAt line 11
2. theorem OAI.Ostmann.HistoryFormula.integralAt_iff line 14
3. theorem OAI.Ostmann.HistoryPivotStep.valid_iff_integral line 29
4. def OAI.Ostmann.reconstructionTests line 43
5. theorem OAI.Ostmann.reconstructionTests_iff line 52

   Source documentation

   Inductively, the polynomial gates enforce exactly the original integer reconstructions. They are not an independently assumed support predicate.

   theorem reconstructionTests_iff {σ : Type*} (steps : List (HistoryPivotStep σ))
       (env : σ → HistoryFormula σ) (x₀ x : σ → ℤ)
       (henv : ∀ i, (env i).value (fun j => (x₀ j : ℚ)) = x i) :
       (∀ F ∈ reconstructionTests steps env, F.IntegralAt x₀) ↔ ValidIntegerReconstruction steps x := by
   …

   Mentions: OAI.Ostmann.HistoryPivotStep, OAI.Ostmann.HistoryFormula, OAI.Ostmann.reconstructionTests, OAI.Ostmann.ValidIntegerReconstruction