WordPowerOfTwo.nonempty_power_depth: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/word_power_of_two.bend as WordPowerOfTwo
Lines 327-337 of stelliferous@0.0.2.0/proofs/word_power_of_two.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/word_power_of_two.bend&start_line=327&end_line=337

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

# A nonempty checked owner cannot have a power-of-two capacity truncated to
# zero. This recovers the full machine-depth bound from its existing guard.
def nonempty_power_depth(+width: Nat,+depth: Nat,positive: {Nat.is_lt(0n,Word.to_nat(width,power(width,depth))) == True{} : Bool}) ->
  {Nat.is_lt(depth,width) == True{} : Bool}:
  match width:
    case 0n: Empty.absurd({Nat.is_lt(depth,0n) == True{} : Bool},WordEncoding.false_true(positive))
    case 1n+ +rest:
      match depth:
        case 0n: {==}
        case 1n+ +previous:
          nonempty_power_depth(rest,previous,positive_double(Word.to_nat(rest,power(rest,previous)),positive))

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=Empty.absurd
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_power_of_two.bend&name=positive_double
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_power_of_two.bend&name=power