Arith.lt_le_add: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as Arith
Lines 77-79 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&start_line=77&end_line=79

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

# a < c, b <= d: a + b < c + d
def lt_le_add(+a: Nat, +b: Nat, +c: Nat, +d: Nat, +h1: {Nat.is_lt(a, c) == True{} : Bool}, +h2: {Nat.is_le(b, d) == True{} : Bool}) -> {Nat.is_lt(Nat.add(a, b), Nat.add(c, d)) == True{} : Bool}:
  N.lt_le_trans(Nat.add(a, b), Nat.add(c, b), Nat.add(c, d), N.lt_add_r2(a, c, b, h1), N.le_add_left(b, d, c, h2))

Uses (8):
  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=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_add_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_add_r2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans