U32.shl_value: 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 118-123 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=118&end_line=123

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_value(+x: U32, +k: Nat, +hk: {Nat.is_le(k, 32n) == True{} : Bool}, +h: {Nat.is_lt(Nat.double(U32.to_nat(x)), SC.pow2(k)) == True{} : Bool}) -> {U32.to_nat(U32.shl(x)) == Nat.double(U32.to_nat(x)) : Nat}:
  match x:
    case U32{+w}:
      %Equal.sym(Nat, U32.to_nat(U32{w}), S.unsigned(32n, w), to_nat_word(w)) : {U32.to_nat(U32{Word.shl(32n, w)}) == Nat.double(_) : Nat}
      Equal.trans(Nat, U32.to_nat(U32{Word.shl(32n, w)}), S.unsigned(32n, Word.shl(32n, w)), Nat.double(S.unsigned(32n, w)), to_nat_word(Word.shl(32n, w)),
        shl_exact_k(32n, k, w, hk, shl_bound(w, k, h)))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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_le
  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.shl
  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.shl
  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=shl_bound
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=shl_exact_k
  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