WordValue.remainder_bit: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/word_value.bend as WordValue
Lines 64-70 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/word_value.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/word_value.bend&start_line=64&end_line=70

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

def remainder_bit(r: Nat, le: {Nat.is_le(r, 1n) == True{} : Bool}) -> {S.bit_value(Nat.is_eq(r, 1n)) == r : Nat}:
  match r:
    case 0n: {==}
    case 1n+x:
      match x:
        case 0n: {==}
        case 1n+y: Empty.absurd({S.bit_value(Nat.is_eq(2n+y, 1n)) == 2n+y : Nat}, Routing.false_true(le))

Uses (7):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  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/lib/lemmas/proofs/map_routing.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=bit_value