Reduce.k38_le_t: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/reduce.bend as Reduce
Lines 62-66 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/reduce.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/reduce.bend&start_line=62&end_line=66

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/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fold.bend as FD

def k38_le_t(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(Nat.add(WD.sc(27n, one), 38n), LM.shn(32n, one)) == True{} : Bool}:
  +a = N.le_trans(38n, 255n, WD.sc(27n, one), {==}, FD.le255(one, h1, 19n))
  +b = M.le_add2(WD.sc(27n, one), 38n, WD.sc(27n, one), WD.sc(27n, one), N.le_refl(WD.sc(27n, one)), a)
  +c = L.subst(Nat, z => {Nat.is_le(Nat.add(WD.sc(27n, one), 38n), z) == True{} : Bool}, Nat.add(WD.sc(27n, one), WD.sc(27n, one)), WD.sc(28n, one), M.sc_dbl(27n, one), b)
  N.le_trans(Nat.add(WD.sc(27n, one), 38n), WD.sc(28n, one), LM.shn(32n, one), c, M.sc_mono(228n, 28n, one))

Uses (13):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fold.bend&name=le255
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=shn
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=le_add2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=sc_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=sc_mono
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc