Nat.bit_split_val: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 372-381 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=372&end_line=381

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

def bit_split_val(+b: Bool, +c: Bool, +u: Nat, +v: Nat, e: {Nat.add(S.bit_value(b), Nat.double(u)) == Nat.add(S.bit_value(c), Nat.double(v)) : Nat}) -> {u == v : Nat}:
  match b c:
    case False{} False{}:
      double_inj(u, v, e)
    case True{} True{}:
      double_inj(u, v, succ_inj(Nat.double(u), Nat.double(v), e))
    case False{} True{}:
      Empty.absurd({u == v : Nat}, even_odd(u, v, e))
    case True{} False{}:
      Empty.absurd({u == v : Nat}, even_odd(v, u, Equal.sym(Nat, 1n+Nat.double(u), Nat.double(v), e)))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=bit_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=double_inj
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=even_odd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_inj