Xbits.or_le32: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend as Xbits
Lines 134-140 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&start_line=134&end_line=140

import Base
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/lib/u32div.bend as UD

def or_le32(+x: U32, +m: U32) -> {Nat.is_le(v(U32.or(x, m)), Nat.add(v(x), v(m))) == True{} : Bool}:
  match x m:
    case U32{+a} U32{+b}:
      %Equal.sym(Nat, UD.v(U32{Word.or(32n, a, b)}), WD.uw(32n, Word.or(32n, a, b)), UD.vw(Word.or(32n, a, b))) : {Nat.is_le(_, Nat.add(v(U32{a}), v(U32{b}))) == True{} : Bool}
      %Equal.sym(Nat, UD.v(U32{a}), WD.uw(32n, a), UD.vw(a)) : {Nat.is_le(WD.uw(32n, Word.or(32n, a, b)), Nat.add(_, v(U32{b}))) == True{} : Bool}
      %Equal.sym(Nat, UD.v(U32{b}), WD.uw(32n, b), UD.vw(b)) : {Nat.is_le(WD.uw(32n, Word.or(32n, a, b)), Nat.add(WD.uw(32n, a), _)) == True{} : Bool}
      or_le(32n, a, b)

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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.or
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=or_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=vw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=uw