Num.le_add_r: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as Num
Lines 72-77 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&start_line=72&end_line=77

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

# x <= a -> x + y <= a + y
def le_add_r(+x: Nat, +a: Nat, +y: Nat, +h: {Nat.is_le(x, a) == True{} : Bool}) -> {Nat.is_le(Nat.add(x, y), Nat.add(a, y)) == True{} : Bool}:
  +e1 = N.le_add_left(x, a, y, h)
  %NA.add_comm(y, x) : {Nat.is_le(_, Nat.add(a, y)) == True{} : Bool}
  %NA.add_comm(y, a) : {Nat.is_le(Nat.add(y, x), _) == True{} : Bool}
  e1

Uses (6):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_add_left