U32half.shr_bridge: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend as U32half
Lines 112-120 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend&start_line=112&end_line=120

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def shr_bridge(+i: Nat, +k: Nat, +hk: {Nat.is_le(k, 32n) == True{} : Bool}, +hi: {Nat.is_lt(i, SC.pow2(k)) == True{} : Bool}) -> {U32.shr(U32.from_nat(i)) == U32.from_nat(hlf(i)) : U32}:
  +ri = U.to_nat_from_nat(i, k, hk, hi)
  U.injective(U32.shr(U32.from_nat(i)), U32.from_nat(hlf(i)),
    Equal.trans(Nat, U32.to_nat(U32.shr(U32.from_nat(i))), hlf(i), U32.to_nat(U32.from_nat(hlf(i))),
      Equal.trans(Nat, U32.to_nat(U32.shr(U32.from_nat(i))), hlf(U32.to_nat(U32.from_nat(i))), hlf(i),
        shr_value(U32.from_nat(i)),
        Equal.cong(Nat, Nat, hlf, U32.to_nat(U32.from_nat(i)), i, ri)),
      Equal.sym(Nat, U32.to_nat(U32.from_nat(hlf(i))), hlf(i),
        U.to_nat_from_nat(hlf(i), k, hk, hlf_bound(i, k, hi)))))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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.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.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shr
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=injective
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=to_nat_from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend&name=hlf
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend&name=hlf_bound
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend&name=shr_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2