Prime.c_two: 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 120-125 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=120&end_line=125

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/spec/math/number.bend as SN

def c_two(+n: Nat, +dq: Nat, +eq: Nat, +qq: Nat, +hn: {n == Nat.mul(2n+qq, 2n+eq) : Nat}, +hdd: {Nat.is_lt(n, Nat.mul(2n+dq, 2n+dq)) == True{} : Bool}, +hs: {SN.nodiv(dq, n, 2n) == True{} : Bool}, +hde: {Nat.is_le(2n+dq, 2n+eq) == True{} : Bool}, +c: Bool, +hc: {Nat.is_lt(2n+qq, 2n+dq) == c : Bool}) -> Empty:
  match c:
    case True{}:
      c_small(n, dq, eq, qq, hn, hs, hc)
    case False{}:
      c_big(n, dq, eq, 2n+qq, hn, hdd, hde, N.not_lt_le(2n+qq, 2n+dq, hc))

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=Empty
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=not_lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend&name=c_big
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend&name=c_small
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/number.bend&name=nodiv