Prime.is_prime_value: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend as Prime
Lines 200-208 of bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend&start_line=200&end_line=208

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/src/math/number.bend as NB
import bend-collections-laws-math@1.0.0.0/spec/math/number.bend as SN

def is_prime_value(+n: Nat) -> SN.IsPrime.value(n):
  match n:
    case 0n:
      {==}
    case 1n:
      {==}
    case 2n+ +p:
      %N.sub_zero(p) : {NB.is_prime(2n+p) == SN.nodiv(_, 2n+p, 2n) : Bool}
      loop(2n+p, 2n+p, 0n, Nat.is_lt(2n+p, 4n), {==}, Nat.is_eq(Nat.mod(2n+p, 2n), 0n), {==}, {==}, {==})

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend&name=loop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/number.bend&name=IsPrime.value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/number.bend&name=nodiv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/number.bend&name=is_prime