StorageAddressBounds.capacity_value: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/storage_address_bounds.bend as StorageAddressBounds
Lines 22-26 of stelliferous@0.0.2.0/proofs/storage_address_bounds.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/storage_address_bounds.bend&start_line=22&end_line=26

import Base
import stelliferous@0.0.2.0/proofs/storage_shape.bend as Shape
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding
import stelliferous@0.0.2.0/proofs/word_power_of_two.bend as Power
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order

def capacity_value(+depth: Nat,limit: {Nat.is_le(depth,31n) == True{} : Bool}) ->
  {U32.to_nat(capacity(depth)) == Shape.extent(depth) : Nat}:
  %Equal.sym(U32,capacity(depth),U32{Power.power(32n,depth)},Power.native_power(depth)) : {U32.to_nat(_) == Shape.extent(depth) : Nat}
  Equal.trans(Nat,Word.to_nat(32n,Power.power(32n,depth)),WordEncoding.shift(depth,1n),Shape.extent(depth),
    Power.power_value(32n,depth,Order.lt_succ(depth,31n,limit)),shift_extent(depth))

Uses (16):
  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=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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  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/nat_order.bend&name=lt_succ
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_address_bounds.bend&name=capacity
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_address_bounds.bend&name=shift_extent
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_shape.bend&name=extent
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_power_of_two.bend&name=native_power
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_power_of_two.bend&name=power
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_power_of_two.bend&name=power_value