Pmul.lbits: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend as Pmul
Lines 36-42 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&start_line=36&end_line=42

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/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsrel.bend as BR

# the bits of a scalar's limbs are the specification's bits of its value
def lbits(+one: Nat, +h1: {one == 1n : Nat}, +ks: List<&2, Nat>, +hk: {FS.limbs16(one, 16n, ks) == True{} : Bool}) -> {L.bits(ks) == CV.bits(256n, FS.value(one, ks)) : List<&2, Nat>}:
  %Equal.sym(List<&2, Nat>, L.bits(ks), BR.sb(256n, 0n, LV.ev(ks)), BR.bits_sb(one, h1, 16n, ks, hk)) : {_ == CV.bits(256n, FS.value(one, ks)) : List<&2, Nat>}
  %Equal.sym(List<&2, Nat>, CV.bits(256n, FS.value(one, ks)), CV.bits_go(256n, FS.value(one, ks)), bits_is(256n, FS.value(one, ks))) : {BR.sb(256n, 0n, LV.ev(ks)) == _ : List<&2, Nat>}
  %Equal.sym(List<&2, Nat>, CV.bits_go(256n, FS.value(one, ks)), BR.sb(256n, 0n, FS.value(one, ks)), go_sb(256n, FS.value(one, ks))) : {BR.sb(256n, 0n, LV.ev(ks)) == _ : List<&2, Nat>}
  %Equal.sym(Nat, FS.value(one, ks), LV.ev(ks), LV.ev_value(one, h1, ks)) : {BR.sb(256n, 0n, LV.ev(ks)) == BR.sb(256n, 0n, _) : List<&2, Nat>}
  {==}

Uses (15):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsrel.bend&name=bits_sb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsrel.bend&name=sb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=ev_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=bits_is
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=go_sb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=bits_go
  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=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=bits