Array.sub_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 215-218 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=215&end_line=218

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
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 sub_bridge(+i: U32, +p: Nat, +hp: {Nat.is_lt(p, 32n) == True{} : Bool}, +le: {Nat.is_le(SC.pow2(p), U32.to_nat(i)) == True{} : Bool}) -> {U32.to_nat(U32.sub(i, U.pow2u(p))) == Nat.sub(U32.to_nat(i), SC.pow2(p)) : Nat}:
  Equal.trans(Nat, U32.to_nat(U32.sub(i, U.pow2u(p))), Nat.sub(U32.to_nat(i), U32.to_nat(U.pow2u(p))), Nat.sub(U32.to_nat(i), SC.pow2(p)),
    U.sub_nat(i, U.pow2u(p), L.subst(Nat, n => {Nat.is_le(n, U32.to_nat(i)) == True{} : Bool}, 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)), le)),
    Equal.cong(Nat, Nat, n => Nat.sub(U32.to_nat(i), n), U32.to_nat(U.pow2u(p)), SC.pow2(p), U.pow2u_value(p, hp)))

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.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=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  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/logic.bend&name=subst
  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/proofs/lib/u32.bend&name=sub_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2