def cn_hb1

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:191

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

191def cn_hb1(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(Nat.mul(1n+FS.cn(one), FS.cn(one)), Nat.mul(4n, C.shift(256n, one))) == True{} : Bool}:
192  +c = FS.cn(one)
193  +s1 = I.le_mul2(1n+c, c, C.shift(129n, one), C.shift(129n, one), N.lt_succ_le_succ(c, C.shift(129n, one), cn_lt(one, h1)), N.lt_le(c, C.shift(129n, one), cn_lt(one, h1)))
194  +s2 = I.le_subst_r(Nat.mul(1n+c, c), Nat.mul(C.shift(129n, one), C.shift(129n, one)), C.shift(258n, one), shift_mul2(one, h1, 129n, 129n), s1)
195  I.le_subst_r(Nat.mul(1n+c, c), C.shift(258n, one), Nat.mul(4n, C.shift(256n, one)), four_t(one), s2)