def cp_hb

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:92

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

92def cp_hb(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(Nat.add(Nat.mul(1n+FS.cp(one), FS.cp(one)), FS.cp(one)), C.shift(256n, one)) == True{} : Bool}:
93  +c = FS.cp(one)
94  +s1 = I.le_mul2(1n+c, c, C.shift(34n, one), C.shift(33n, one), cp_succ_le(one, h1), cp_le(one, h1))
95  +s2 = I.le_subst_r(Nat.mul(1n+c, c), Nat.mul(C.shift(34n, one), C.shift(33n, one)), C.shift(67n, one), shift_mul2(one, h1, 34n, 33n), s1)
96  +s3 = I.le_add2(Nat.mul(1n+c, c), c, C.shift(67n, one), C.shift(67n, one), s2, N.le_trans(c, C.shift(33n, one), C.shift(67n, one), cp_le(one, h1), shift_le_k(33n, 67n, one, 34n, {==})))
97  +s4 = I.le_subst_r(Nat.add(Nat.mul(1n+c, c), c), Nat.add(C.shift(67n, one), C.shift(67n, one)), C.shift(68n, one), shift_twice(67n, one), s3)
98  N.le_trans(Nat.add(Nat.mul(1n+c, c), c), C.shift(68n, one), C.shift(256n, one), s4, shift_le_k(68n, 256n, one, 188n, {==}))