def cp_lt_cn

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/rconst.bend:48

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/consts.bend as K

48def cp_lt_cn(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_lt(FS.cp(one), FS.cn(one)) == True{} : Bool}:
49  N.le_lt_trans(FS.cp(one), C.shift(33n, one), FS.cn(one), K.cp_le(one, h1), N.lt_le_trans(C.shift(33n, one), C.shift(128n, one), FS.cn(one), K.shift_lt_k(one, h1, 33n, 128n, 94n, {==}), cn_ge(one, h1)))