DivisionQuotient.below_successor: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_quotient.bend as DivisionQuotient
Lines 14-20 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_quotient.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_quotient.bend&start_line=14&end_line=20

import Base

def below_successor(r: Nat, p: Nat) -> {Nat.is_lt(r, 1n+p) == Nat.is_le(r, p) : Bool}:
  match r p:
    case 0n 0n: {==}
    case 0n 1n+k: {==}
    case 1n+0n 0n: {==}
    case 1n+1n+j 0n: {==}
    case 1n+k 1n+j: below_successor(k, j)

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt