def one_le_sc

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:30

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/limbs.bend as LM

30def one_le_sc(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat) -> {Nat.is_le(one, WD.sc(n, one)) == True{} : Bool}:
31  +a = N.lt_succ_le_succ(0n, WD.sc(n, one), LM.sc_pos1(n, one, h1))
32  L.subst(Nat, o => {Nat.is_le(o, WD.sc(n, one)) == True{} : Bool}, 1n, one, Equal.sym(Nat, one, 1n, h1), a)