Paff.lt_p_red: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend as Paff
Lines 73-75 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend&start_line=73&end_line=75

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fwrap.bend as FW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

def lt_p_red(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +hl: {FS.limbs16(one, 16n, x) == True{} : Bool}, +h: {F.lt_p(x) == True{} : Bool}) -> {PT.red(one, x) == True{} : Bool}:
  +hv = Equal.trans(Bool, Nat.is_lt(FS.value(one, x), FS.prime(one)), F.lt_p(x), True{}, Equal.sym(Bool, F.lt_p(x), Nat.is_lt(FS.value(one, x), FS.prime(one)), FW.lt_p_f(one, h1, x)), h)
  Lg.and_intro(FS.limbs16(one, 16n, x), Nat.is_lt(FS.value(one, x), FS.prime(one)), hl, hv)

Uses (13):
  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=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fwrap.bend&name=lt_p_f
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=red
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=limbs16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=lt_p