Fieldops.le_small: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as Fieldops
Lines 36-39 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&start_line=36&end_line=39

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

# 255 + 255 and 255 + 2040 are below 2^28
def 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}:
  +a = L.subst(Nat, o => {Nat.is_le(4096n, WD.sc(12n, o)) == True{} : Bool}, 1n, one, Equal.sym(Nat, one, 1n, h1), {==})
  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))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=sc_mono
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc