Poly.addl_len_le: 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 168-179 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=168&end_line=179

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

def addl_len_le(+n: Nat, +xs: List<&2, U32>, +ys: List<&2, U32>, +ex: {len_le(n, xs) == True{} : Bool}, +ey: {len_le(n, ys) == True{} : Bool}) -> {len_le(n, F.addl(xs, ys)) == True{} : Bool}:
  match n xs ys:
    case 0n Nil{} _:
      ey
    case 0n Con{x, xt} _:
      Empty.absurd({len_le(0n, F.addl(Con{x, xt}, ys)) == True{} : Bool}, L.false_true(ex))
    case 1n+m Nil{} _:
      ey
    case 1n+m Con{x, xt} Nil{}:
      ex
    case 1n+ +m Con{x, +xt} Con{y, +yt}:
      addl_len_le(m, xt, yt, ex, ey)

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=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=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend&name=len_le
  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/src/crypto/curve25519/field.bend&name=addl