Consts.cp_eq: 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 58-67 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=58&end_line=67

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

def cp_eq(+one: Nat, +h1: {one == 1n : Nat}) -> {FS.cp(one) == Nat.add(C.shift(32n, one), 977n) : Nat}:
  %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}
  %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}
  %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}
  %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}
  %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}
  %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}
  %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}
  %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}
  {==}

Uses (14):
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=mul_one_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend&name=shift_shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend&name=zero_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  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=mul_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=cp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift