def four_t

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:184

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

184def four_t(+one: Nat) -> {C.shift(258n, one) == Nat.mul(4n, C.shift(256n, one)) : Nat}:
185  %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}
186  %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}
187  %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}
188  %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}
189  {==}