ProofShift.ns.le_add_mono_r: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 182-185 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=182&end_line=185

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL
import bend-osdev-word64@0.1.1.0/proof_value.bend as P

def ns.le_add_mono_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}:
  %UL.nat_add_comm(c, a) : {Nat.is_le(_, Nat.add(b, c)) == True{} : Bool}
  %UL.nat_add_comm(c, b) : {Nat.is_le(Nat.add(c, a), _) == True{} : Bool}
  Equal.trans(Bool, Nat.is_le(Nat.add(c, a), Nat.add(c, b)), Nat.is_le(a, b), True{}, P.wn.le_add_l(c, a, b), 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.trans
  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-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.le_add_l