U32int.pmon: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32int.bend as U32int
Lines 832-834 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32int.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32int.bend&start_line=832&end_line=834

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend as NF
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S

def pmon(+nn: Nat, +j: Nat, +r: Nat, +k0: Nat, +hj: {Nat.add(j, r) == k0 : Nat}, +hle: {Nat.is_le(k0, nn) == True{} : Bool}) -> {Nat.is_le(S.desc(nn, j), S.desc(nn, k0)) == True{} : Bool}:
  +h1 = NF.dmono(nn, j, r, L.subst(Nat, z => {Nat.is_le(z, nn) == True{} : Bool}, k0, Nat.add(j, r), Equal.sym(Nat, Nat.add(j, r), k0, hj), hle))
  L.subst(Nat, z => {Nat.is_le(S.desc(nn, j), S.desc(nn, z)) == True{} : Bool}, Nat.add(j, r), k0, hj, h1)

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=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-math@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend&name=dmono
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=desc