def le_small

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fieldops.bend:36

import Base
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/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M

36# 255 + 255 and 255 + 2040 are below 2^28
37def le_small(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat, +hx: {Nat.is_le(x, 4096n) == True{} : Bool}) -> {Nat.is_le(x, WD.sc(28n, one)) == True{} : Bool}:
38  +a = L.subst(Nat, o => {Nat.is_le(4096n, WD.sc(12n, o)) == True{} : Bool}, 1n, one, Equal.sym(Nat, one, 1n, h1), {==})
39  N.le_trans(x, WD.sc(12n, one), WD.sc(28n, one), N.le_trans(x, 4096n, WD.sc(12n, one), hx, a), M.sc_mono(16n, 12n, one))