Lists.lt_pow2: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend as Lists
Lines 96-101 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend&start_line=96&end_line=101

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/spec/lib/common.bend as SC

# 2^h is strictly above h - 1, i.e. n < 2^(n+1).
def lt_pow2(+n: Nat) -> {Nat.is_lt(n,SC.pow2(n)) == True{} : Bool}:
  match n:
    case 0n: {==}
    case 1n+q:
      N.lt_le_trans(1n+q,1n+SC.pow2(q),Nat.double(SC.pow2(q)),lt_pow2(q),N.double_succ_le(SC.pow2(q),N.pow2_pos(q)))

Uses (8):
  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.double
  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/nat.bend&name=double_succ_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=pow2_pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2