def cp_cc

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:82

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

82# the fold bounds for p: 2 c < 2^256 and (1 + c) c + c <= 2^256
83def cp_cc(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_lt(Nat.add(FS.cp(one), FS.cp(one)), C.shift(256n, one)) == True{} : Bool}:
84  +c = FS.cp(one)
85  +s1 = I.le_add2(c, c, C.shift(33n, one), C.shift(33n, one), cp_le(one, h1), cp_le(one, h1))
86  +s2 = I.le_subst_r(Nat.add(c, c), Nat.add(C.shift(33n, one), C.shift(33n, one)), C.shift(34n, one), shift_twice(33n, one), s1)
87  N.le_lt_trans(Nat.add(c, c), C.shift(34n, one), C.shift(256n, one), s2, shift_lt_k(one, h1, 34n, 256n, 221n, {==}))