Consts.four_t: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as Consts
Lines 184-189 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&start_line=184&end_line=189

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

def four_t(+one: Nat) -> {C.shift(258n, one) == Nat.mul(4n, C.shift(256n, one)) : Nat}:
  %Equal.sym(Nat, Nat.double(C.shift(256n, one)), Nat.add(C.shift(256n, one), C.shift(256n, one)), NA.double_self(C.shift(256n, one))) : {Nat.double(_) == Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), 0n)))) : Nat}
  %Equal.sym(Nat, Nat.double(Nat.add(C.shift(256n, one), C.shift(256n, one))), Nat.add(Nat.add(C.shift(256n, one), C.shift(256n, one)), Nat.add(C.shift(256n, one), C.shift(256n, one))), NA.double_self(Nat.add(C.shift(256n, one), C.shift(256n, one)))) : {_ == Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), 0n)))) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.add(C.shift(256n, one), C.shift(256n, one)), Nat.add(C.shift(256n, one), C.shift(256n, one))), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), C.shift(256n, one)))), NA.add_assoc(C.shift(256n, one), C.shift(256n, one), Nat.add(C.shift(256n, one), C.shift(256n, one)))) : {_ == Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), 0n)))) : Nat}
  %Equal.sym(Nat, Nat.add(C.shift(256n, one), 0n), C.shift(256n, one), NA.add_zero(C.shift(256n, one))) : {Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), C.shift(256n, one)))) == Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), Nat.add(C.shift(256n, one), _))) : Nat}
  {==}

Uses (9):
  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.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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=double_self
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift