Array.lt_bridge: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend as Array
Lines 210-213 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&start_line=210&end_line=213

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 lt_bridge(+i: U32, +p: Nat, +hp: {Nat.is_lt(p, 32n) == True{} : Bool}, +b: Bool, +eb: {U32.is_lt(i, U.pow2u(p)) == b : Bool}) -> {Nat.is_lt(U32.to_nat(i), SC.pow2(p)) == b : Bool}:
  Equal.trans(Bool, Nat.is_lt(U32.to_nat(i), SC.pow2(p)), Nat.is_lt(U32.to_nat(i), U32.to_nat(U.pow2u(p))), b,
    Equal.cong(Nat, Bool, n => Nat.is_lt(U32.to_nat(i), n), SC.pow2(p), U32.to_nat(U.pow2u(p)), Equal.sym(Nat, U32.to_nat(U.pow2u(p)), SC.pow2(p), U.pow2u_value(p, hp))),
    Equal.trans(Bool, Nat.is_lt(U32.to_nat(i), U32.to_nat(U.pow2u(p))), U32.is_lt(i, U.pow2u(p)), b, Equal.sym(Bool, U32.is_lt(i, U.pow2u(p)), Nat.is_lt(U32.to_nat(i), U32.to_nat(U.pow2u(p))), U.is_lt_nat(i, U.pow2u(p))), eb))

Uses (13):
  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_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.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/u32.bend&name=is_lt_nat
  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/proofs/lib/u32.bend&name=pow2u_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2