U32.shl_bound: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U32
Lines 114-116 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&start_line=114&end_line=116

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

def shl_bound(+w: Word(32n), +k: Nat, +h: {Nat.is_lt(Nat.double(U32.to_nat(U32{w})), SC.pow2(k)) == True{} : Bool}) -> {Nat.is_lt(Nat.double(S.unsigned(32n, w)), SC.pow2(k)) == True{} : Bool}:
  %to_nat_word(w) : {Nat.is_lt(Nat.double(_), SC.pow2(k)) == True{} : Bool}
  h

Uses (10):
  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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=to_nat_word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2