def cp_eq

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:58

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/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend as SR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV

58def cp_eq(+one: Nat, +h1: {one == 1n : Nat}) -> {FS.cp(one) == Nat.add(C.shift(32n, one), 977n) : Nat}:
59  %Equal.sym(Nat, Nat.mul(one, 977n), 977n, LV.mul_one_l(one, h1, 977n)) : {Nat.add(_, C.shift(16n, Nat.add(Nat.mul(one, 0n), C.shift(16n, Nat.add(Nat.mul(one, 1n), C.shift(16n, 0n)))))) == Nat.add(C.shift(32n, one), 977n) : Nat}
60  %Equal.sym(Nat, Nat.mul(one, 0n), 0n, NA.mul_zero(one)) : {Nat.add(977n, C.shift(16n, Nat.add(_, C.shift(16n, Nat.add(Nat.mul(one, 1n), C.shift(16n, 0n)))))) == Nat.add(C.shift(32n, one), 977n) : Nat}
61  %Equal.sym(Nat, Nat.mul(one, 1n), one, NA.mul_one(one)) : {Nat.add(977n, C.shift(16n, Nat.add(0n, C.shift(16n, Nat.add(_, C.shift(16n, 0n)))))) == Nat.add(C.shift(32n, one), 977n) : Nat}
62  %Equal.sym(Nat, C.shift(16n, 0n), 0n, WW.shift_zero(16n)) : {Nat.add(977n, C.shift(16n, Nat.add(0n, C.shift(16n, Nat.add(one, _))))) == Nat.add(C.shift(32n, one), 977n) : Nat}
63  %Equal.sym(Nat, Nat.add(one, 0n), one, NA.add_zero(one)) : {Nat.add(977n, C.shift(16n, Nat.add(0n, C.shift(16n, _)))) == Nat.add(C.shift(32n, one), 977n) : Nat}
64  %Equal.sym(Nat, Nat.add(0n, C.shift(16n, one)), C.shift(16n, one), SR.zero_add(C.shift(16n, one))) : {Nat.add(977n, C.shift(16n, _)) == Nat.add(C.shift(32n, one), 977n) : Nat}
65  %Equal.sym(Nat, C.shift(16n, C.shift(16n, one)), C.shift(32n, one), SR.shift_shift(16n, 16n, one)) : {Nat.add(977n, _) == Nat.add(C.shift(32n, one), 977n) : Nat}
66  %Equal.sym(Nat, Nat.add(977n, C.shift(32n, one)), Nat.add(C.shift(32n, one), 977n), NA.add_comm(977n, C.shift(32n, one))) : {_ == Nat.add(C.shift(32n, one), 977n) : Nat}
67  {==}