U32.pow2u_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 161-163 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=161&end_line=163

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

def pow2u_shl_bound(+p: Nat, +ih: {U32.to_nat(pow2u(p)) == SC.pow2(p) : Nat}) -> {Nat.is_lt(Nat.double(U32.to_nat(pow2u(p))), SC.pow2(2n+p)) == True{} : Bool}:
  %Equal.sym(Nat, U32.to_nat(pow2u(p)), SC.pow2(p), ih) : {Nat.is_lt(Nat.double(_), SC.pow2(2n+p)) == True{} : Bool}
  N.pow2_lt_succ(1n+p)

Uses (9):
  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=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.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=pow2_lt_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=pow2u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2