U32.shr_pow2u: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U32
Lines 175-182 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&start_line=175&end_line=182

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

def shr_pow2u(+p: Nat, +h: {Nat.is_lt(1n+p, 32n) == True{} : Bool}) -> {U32.shr(pow2u(1n+p)) == pow2u(p) : U32}:
  injective(U32.shr(pow2u(1n+p)), pow2u(p),
    Equal.trans(Nat, U32.to_nat(U32.shr(pow2u(1n+p))), SC.pow2(p), U32.to_nat(pow2u(p)),
      N.bit_split_val(low_bit(pow2u(1n+p)), False{}, U32.to_nat(U32.shr(pow2u(1n+p))), SC.pow2(p),
        Equal.trans(Nat, Nat.add(S.bit_value(low_bit(pow2u(1n+p))), Nat.double(U32.to_nat(U32.shr(pow2u(1n+p))))), U32.to_nat(pow2u(1n+p)), Nat.double(SC.pow2(p)),
          Equal.sym(Nat, U32.to_nat(pow2u(1n+p)), Nat.add(S.bit_value(low_bit(pow2u(1n+p))), Nat.double(U32.to_nat(U32.shr(pow2u(1n+p))))), shr_split(pow2u(1n+p))),
          pow2u_value(1n+p, h))),
      Equal.sym(Nat, U32.to_nat(pow2u(p)), SC.pow2(p), pow2u_value(p, N.lt_trans(p, 1n+p, 32n, N.lt_succ(p), h)))))

Uses (20):
  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.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_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.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-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=bit_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=bit_split_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=injective
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=low_bit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=pow2u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=pow2u_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=shr_split
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=pow2