def cn_cc

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:177

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/crypto/secp256k1/ineq.bend as I

177# the fold bounds for n: 2 c < 2^256, (1 + c) c <= 4 2^256, 5 c + c <= 2^256
178def cn_cc(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_lt(Nat.add(FS.cn(one), FS.cn(one)), C.shift(256n, one)) == True{} : Bool}:
179  +c = FS.cn(one)
180  +s1 = I.lt_le_add(c, c, C.shift(129n, one), C.shift(129n, one), cn_lt(one, h1), N.lt_le(c, C.shift(129n, one), cn_lt(one, h1)))
181  +s2 = I.lt_subst_r(Nat.add(c, c), Nat.add(C.shift(129n, one), C.shift(129n, one)), C.shift(130n, one), shift_twice(129n, one), s1)
182  N.lt_trans(Nat.add(c, c), C.shift(130n, one), C.shift(256n, one), s2, shift_lt_k(one, h1, 130n, 256n, 125n, {==}))