def prime_eq

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:123

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/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

123def prime_eq(+one: Nat, +h1: {one == 1n : Nat}) -> {FS.prime(one) == 1n+pp(one) : Nat}:
124  %Equal.sym(Nat, C.shift(256n, one), Nat.add(1n+pp(one), FS.cp(one)), Equal.sym(Nat, Nat.add(1n+pp(one), FS.cp(one)), C.shift(256n, one), hm_p(one, h1))) : {Nat.sub(_, FS.cp(one)) == 1n+pp(one) : Nat}
125  %Equal.sym(Nat, Nat.add(1n+pp(one), FS.cp(one)), Nat.add(FS.cp(one), 1n+pp(one)), NA.add_comm(1n+pp(one), FS.cp(one))) : {Nat.sub(_, FS.cp(one)) == 1n+pp(one) : Nat}
126  N.add_sub_cancel(FS.cp(one), 1n+pp(one))