def cn_hb2

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:211

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/arith.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I

211def cn_hb2(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(Nat.add(Nat.mul(5n, FS.cn(one)), FS.cn(one)), C.shift(256n, one)) == True{} : Bool}:
212  +c = FS.cn(one)
213  +l = N.lt_le(c, C.shift(129n, one), cn_lt(one, h1))
214  +s1 = I.le_add2(Nat.mul(5n, c), c, Nat.mul(5n, C.shift(129n, one)), C.shift(129n, one), I.le_mul_r(5n, c, C.shift(129n, one), l), l)
215  +s2 = I.le_subst_r(Nat.add(Nat.mul(5n, c), c), Nat.add(Nat.mul(5n, C.shift(129n, one)), C.shift(129n, one)), Nat.mul(6n, C.shift(129n, one)), six(C.shift(129n, one)), s1)
216  +s3 = N.le_trans(Nat.mul(6n, C.shift(129n, one)), Nat.mul(8n, C.shift(129n, one)), C.shift(132n, one), AR.mul_le(6n, 8n, C.shift(129n, one), {==}), I.le_subst_r(Nat.mul(8n, C.shift(129n, one)), C.shift(132n, one), C.shift(132n, one), {==}, N.eq_le(Nat.mul(8n, C.shift(129n, one)), C.shift(132n, one), eight(C.shift(129n, one)))))
217  N.le_trans(Nat.add(Nat.mul(5n, c), c), Nat.mul(6n, C.shift(129n, one)), C.shift(256n, one), s2, N.le_trans(Nat.mul(6n, C.shift(129n, one)), C.shift(132n, one), C.shift(256n, one), s3, shift_le_k(132n, 256n, one, 124n, {==})))