NatDivision.lt_succ_le: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_division.bend as NatDivision
Lines 13-23 of stelliferous@0.0.2.0/proofs/nat_division.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_division.bend&start_line=13&end_line=23

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def lt_succ_le(+n: Nat,+m: Nat,h: {Nat.is_lt(n,1n+m) == True{} : Bool}) -> {Nat.is_le(n,m) == True{} : Bool}:
  match n m:
    case 0n 0n:
      {==}
    case 0n 1n+m:
      {==}
    case 1n+ +n 0n:
      Empty.absurd({Nat.is_le(1n+n,0n) == True{} : Bool},WordEncoding.false_true(Equal.trans(Bool,False{},Nat.is_lt(n,0n),True{},Equal.sym(Bool,
              Nat.is_lt(n,0n),False{},lt_zero(n)),h)))
    case 1n+n 1n+m:
      lt_succ_le(n,m,h)

Uses (9):
  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=Equal.trans
  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=stelliferous@0.0.2.0/proofs/nat_division.bend&name=lt_zero
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true