def head_le

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fold.bend:64

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

64# 255 + 38 c <= 2^28 for c <= 2^21
65def head_le(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat, +c: Nat, +hx: {Nat.is_le(x, 255n) == True{} : Bool}, +hc: {Nat.is_le(c, WD.sc(21n, one)) == True{} : Bool}) -> {Nat.is_le(Nat.add(x, Nat.mul(38n, c)), WD.sc(28n, one)) == True{} : Bool}:
66  +a = N.le_trans(x, 255n, WD.sc(27n, one), hx, le255(one, h1, 19n))
67  +b0 = N.le_trans(Nat.mul(38n, c), Nat.mul(38n, WD.sc(21n, one)), WD.sc(6n, WD.sc(21n, one)), M.le_mul2(38n, c, 38n, WD.sc(21n, one), N.le_refl(38n), hc), m38(WD.sc(21n, one)))
68  +s = M.le_add2(x, Nat.mul(38n, c), WD.sc(27n, one), WD.sc(27n, one), a, b0)
69  L.subst(Nat, z => {Nat.is_le(Nat.add(x, Nat.mul(38n, c)), z) == True{} : Bool}, Nat.add(WD.sc(27n, one), WD.sc(27n, one)), WD.sc(28n, one), M.sc_dbl(27n, one), s)