Sqrtn.add_two: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/sqrtn.bend as Sqrtn
Lines 31-33 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/sqrtn.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/sqrtn.bend&start_line=31&end_line=33

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/proofs/lib/lemmas/proofs/nat_algebra.bend as A

# (1 + x) + (1 + y) == 2 + (x + y)
def add_two(+x: Nat, +y: Nat) -> {Nat.add(1n+x, 1n+y) == 2n+Nat.add(x, y) : Nat}:
  N.succ_cong(Nat.add(x, 1n+y), 1n+Nat.add(x, y), A.add_succ(x, y))

Uses (4):
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_cong