Fixprime.found_one: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend as Fixprime
Lines 139-141 of bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&start_line=139&end_line=141

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend as SF
import bend-collections-laws-math@1.0.0.0/spec/math/number.bend as SN
import bend-collections-laws-math@1.0.0.0/src/math/fixed.bend as F
import bend-collections-laws-math@1.0.0.0/src/math/number.bend as NB

def found_one(+one: Nat, +h1: {one == 1n : Nat}, +n: U32, +p: U32, +h: {F.u32_next_prime(n) == Some{p} : Maybe<&2, U32>}) -> {Bool.and(Bool.and(Nat.is_le(1n+v(n), v(p)), SN.prime(v(p))), SF.no_prime(Nat.sub(v(p), 1n+v(n)), 1n+v(n))) == True{} : Bool}:
  +m1 = U32.add(n, 1)
  found_go(Nat.add(v(U32.not(n)), 1n), one, h1, m1, U32.is_zero(m1), {==}, NB.is_prime(v(m1)), {==}, 1n+v(n), succ_t(one, h1, n), p, h)

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.not
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=found_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=succ_t
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=no_prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/number.bend&name=prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/fixed.bend&name=u32_next_prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/number.bend&name=is_prime