Memory.lt_sub: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend as Memory
Lines 207-214 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&start_line=207&end_line=214

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

def lt_sub(+base: Nat, +k: Nat, +n: Nat, +h: {Nat.is_lt(Nat.add(base, k), n) == True{} : Bool}) -> {Nat.is_lt(k, Nat.sub(n, base)) == True{} : Bool}:
  match base n:
    case 0n _:
      L.subst(Nat, z => {Nat.is_lt(k, z) == True{} : Bool}, n, Nat.sub(n, 0n), Equal.sym(Nat, Nat.sub(n, 0n), n, N.sub_zero(n)), h)
    case 1n+b 0n:
      Empty.absurd({Nat.is_lt(k, Nat.sub(0n, 1n+b)) == True{} : Bool}, N.lt_zero_absurd(Nat.add(1n+b, k), h))
    case 1n+ +b 1n+ +m:
      lt_sub(b, k, m, h)

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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=sub_zero