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bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | import compcert.lib.ZArithCompat
import AUXLib.ListLib
namespace Algorithms.linear_modular_inverse.lean
open AUXLib
def PrimeForLinearInverse (p : Int) : Prop :=
2 ≤ p ∧ ∀ divisor, (2 ≤ divisor ∧ divisor < p) → Z.modulo p divisor ≠ 0
def CanonicalModularInverse (p index value : Int) : Prop :=
(1 ≤ index ∧ index < p) ∧ (0 < value ∧ value < p) ∧
∃ coefficient, index * value + p * coefficient = 1
def ModularInversePrefix (p next : Int) (values : List Int) : Prop :=
Zlength values = next - 1 ∧ ∀ index, (1 ≤ index ∧ index < next) →
CanonicalModularInverse p index (Znth (index - 1) values 0)
end Algorithms.linear_modular_inverse.lean
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