Fixprime.found: 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 143-146 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=143&end_line=146

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

def found(+n: U32, +p: U32, +h: {F.u32_next_prime(n) == Some{p} : Maybe<&2, U32>}) -> SF.NextPrime.found(n, p, h):
  +g = found_one(1n, {==}, n, p, h)
  %Equal.sym(Bool, Nat.is_lt(v(n), v(p)), Nat.is_le(1n+v(n), v(p)), lt_iff(v(n), v(p))) : {Bool.and(Bool.and(_, SN.prime(v(p))), SF.no_prime(Nat.sub(v(p), 1n+v(n)), 1n+v(n))) == True{} : Bool}
  g

Uses (16):
  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=Equal.sym
  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.is_le
  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.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=found_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=lt_iff
  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=NextPrime.found
  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