Memory.lt_pred: 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 236-237 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=236&end_line=237

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_pred(+base: Nat, +p: Nat, +n: Nat, +h: {Nat.is_lt(Nat.add(base, 1n+p), n) == True{} : Bool}) -> {Nat.is_lt(Nat.add(base, p), n) == True{} : Bool}:
  N.lt_trans(Nat.add(base, p), Nat.add(base, 1n+p), n, L.subst(Nat, z => {Nat.is_lt(Nat.add(base, p), z) == True{} : Bool}, 1n+Nat.add(base, p), Nat.add(base, 1n+p), Equal.sym(Nat, Nat.add(base, 1n+p), 1n+Nat.add(base, p), N.add_succ(base, p)), N.lt_succ(Nat.add(base, p))), 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=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=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=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_trans