Lemire.le_succ_lt: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as Lemire
Lines 178-188 of bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&start_line=178&end_line=188

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

# a + 1 <= b is a < b
def le_succ_lt(+a: Nat, +b: Nat) -> {Nat.is_le(1n+a, b) == Nat.is_lt(a, b) : Bool}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      N.zero_le(q)
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      le_succ_lt(p, q)

Uses (5):
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=zero_le