Logs.le_add_r: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/logs.bend as Logs
Lines 14-18 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/logs.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/logs.bend&start_line=14&end_line=18

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 A

# a <= b gives a + c <= b + c
def le_add_r(+a: Nat, +b: Nat, +c: Nat, +h: {Nat.is_le(a, b) == True{} : Bool}) -> {Nat.is_le(Nat.add(a, c), Nat.add(b, c)) == True{} : Bool}:
  %Equal.sym(Nat, Nat.add(a, c), Nat.add(c, a), A.add_comm(a, c)) : {Nat.is_le(_, Nat.add(b, c)) == True{} : Bool}
  %Equal.sym(Nat, Nat.add(b, c), Nat.add(c, b), A.add_comm(b, c)) : {Nat.is_le(Nat.add(c, a), _) == True{} : Bool}
  N.le_add_left(a, b, c, h)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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