def le_bytes_ok

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/ed25519/pdec.bend:163

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/x25519.bend as SX
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/u32.bend as U
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as NR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

163def le_bytes_ok(+n: Nat, +x: Nat) -> {LM.okb(n, SX.le_bytes(n, x), 255n) == True{} : Bool}:
164  match n:
165    case 0n:
166      {==}
167    case 1n+ +m:
168      +r = Nat.mod(x, 256n)
169      +hr = NR.dm_lt(255n, x)
170      +e = U.to_nat_from_nat(r, 8n, {==}, hr)
171      +h = L.subst(Nat, z => {Nat.is_le(z, 255n) == True{} : Bool}, r, v(U32.from_nat(r)), Equal.sym(Nat, v(U32.from_nat(r)), r, e), N.lt_succ_le(r, 255n, hr))
172      L.and_intro(Nat.is_le(v(U32.from_nat(r)), 255n), LM.okb(m, SX.le_bytes(m, Nat.div(x, 256n)), 255n), h, le_bytes_ok(m, Nat.div(x, 256n)))