Poly.okb_mono: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend as Poly
Lines 90-99 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend&start_line=90&end_line=99

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/crypto/curve25519/limbs.bend as LM

def okb_mono(+n: Nat, +xs: List<&2, U32>, +b: Nat, +c: Nat, +hb: {Nat.is_le(b, c) == True{} : Bool}, +e: {LM.okb(n, xs, b) == True{} : Bool}) -> {LM.okb(n, xs, c) == True{} : Bool}:
  match n xs:
    case 0n Nil{}:
      {==}
    case 0n Con{y, yt}:
      Empty.absurd({LM.okb(0n, Con{y, yt}, c) == True{} : Bool}, L.false_true(e))
    case 1n+m Nil{}:
      Empty.absurd({LM.okb(1n+m, Nil{}, c) == True{} : Bool}, L.false_true(e))
    case 1n+ +m Con{+y, +yt}:
      L.and_intro(Nat.is_le(v(y), c), LM.okb(m, yt, c), N.le_trans(v(y), b, c, LM.okb_head(m, y, yt, b, e), hb), okb_mono(m, yt, b, c, hb, LM.okb_tail(m, y, yt, b, e)))

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=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb_head
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb_tail
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans