Consts.shift_more: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as Consts
Lines 28-34 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&start_line=28&end_line=34

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

# 2^k x <= 2^(d + k) x
def shift_more(d: Nat, +k: Nat, +x: Nat) -> {Nat.is_le(C.shift(k, x), C.shift(Nat.add(d, k), x)) == True{} : Bool}:
  match d:
    case 0n:
      N.le_refl(C.shift(k, x))
    case 1n+ +e:
      N.le_trans(C.shift(k, x), C.shift(Nat.add(e, k), x), Nat.double(C.shift(Nat.add(e, k), x)), shift_more(e, k, x), N.double_self_le(C.shift(Nat.add(e, k), x)))

Uses (9):
  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.double
  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/lib/nat.bend&name=double_self_le
  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/spec/lib/common.bend&name=shift