Xbits.clamp_top_okb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend as Xbits
Lines 142-156 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&start_line=142&end_line=156

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/x25519.bend as X
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/math/hash/hash.bend as HH
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

def clamp_top_okb(+n: Nat, +xs: List<&2, U32>, +e: {LM.okb(1n+n, xs, 255n) == True{} : Bool}) -> {LM.okb(1n+n, X.clamp_top(xs), 255n) == True{} : Bool}:
  match n xs:
    case _ Nil{}:
      Empty.absurd({LM.okb(1n+n, Nil{}, 255n) == True{} : Bool}, L.false_true(e))
    case 0n Con{+x, Nil{}}:
      +a = HH.and_le32(x, 127)
      +o = or_le32(U32.and(x, 127), 64)
      +b = N.le_trans(v(U32.or(U32.and(x, 127), 64)), Nat.add(v(U32.and(x, 127)), 64n), 255n, o, N.le_trans(Nat.add(v(U32.and(x, 127)), 64n), Nat.add(127n, 64n), 255n, M.le_add_r(v(U32.and(x, 127)), 127n, 64n, a), {==}))
      L.and_intro(Nat.is_le(v(U32.or(U32.and(x, 127), 64)), 255n), True{}, b, {==})
    case 0n Con{x, Con{y, yt}}:
      Empty.absurd({LM.okb(1n, X.clamp_top(Con{x, Con{y, yt}}), 255n) == True{} : Bool}, L.false_true(LM.okb_tail(0n, x, Con{y, yt}, 255n, e)))
    case 1n+m Con{x, Nil{}}:
      Empty.absurd({LM.okb(2n+m, X.clamp_top(Con{x, Nil{}}), 255n) == True{} : Bool}, L.false_true(LM.okb_tail(1n+m, x, Nil{}, 255n, e)))
    case 1n+ +m Con{+x, Con{+y, +yt}}:
      L.and_intro(Nat.is_le(v(x), 255n), LM.okb(1n+m, X.clamp_top(Con{y, yt}), 255n), LM.okb_head(1n+m, x, Con{y, yt}, 255n, e), clamp_top_okb(m, Con{y, yt}, LM.okb_tail(1n+m, x, Con{y, yt}, 255n, e)))

Uses (20):
  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.add
  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=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.or
  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/num.bend&name=le_add_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=or_le32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/hash/hash.bend&name=and_le32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/x25519.bend&name=clamp_top