U32Shift.encoded_shift: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/u32_shift.bend as U32Shift
Lines 49-52 of stelliferous@0.0.2.0/proofs/u32_shift.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/u32_shift.bend&start_line=49&end_line=52

import Base
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition
import stelliferous@0.0.2.0/proofs/word_arithmetic.bend as WordArithmetic
import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as Arithmetic

def encoded_shift(+w: Word(32n)) -> {U32{Word.shl(32n,w)} == U32.from_nat(Nat.double(Word.to_nat(32n,w))) : U32}:
  %WordArithmetic.double_word(32n,w) : {U32{_} == U32.from_nat(Nat.double(Word.to_nat(32n,w))) : U32}
  %Addition.double(Word.to_nat(32n,w)) : {U32{Word.add(32n,w,w)} == U32.from_nat(_) : U32}
  Arithmetic.native_add(U32{w},U32{w})

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&name=native_add
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=double
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_arithmetic.bend&name=double_word