def pmon

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u32int.bend:832

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

832def 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}:
833  +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))
834  L.subst(Nat, z => {Nat.is_le(S.desc(nn, j), S.desc(nn, z)) == True{} : Bool}, Nat.add(j, r), k0, hj, h1)