StorageAddressBounds.right_restores_index_full: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/storage_address_bounds.bend as StorageAddressBounds
Lines 48-56 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=48&end_line=56

import Base
import stelliferous@0.0.2.0/proofs/storage_shape.bend as Shape
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order
import stelliferous@0.0.2.0/proofs/word_subtraction.bend as Subtraction

def right_restores_index_full(+depth: Nat,+index: U32,+limit: {Nat.is_le(1n+depth,31n) == True{} : Bool},+bound: {U32.is_lt(index,capacity(1n+depth)) == True{} : Bool},
  +choice: {U32.is_lt(index,capacity(depth)) == False{} : Bool}) -> {U32.to_nat(index) == Nat.add(Shape.extent(depth),U32.to_nat((index - capacity(depth) : U32))) : Nat}:
  %Equal.sym(Nat,U32.to_nat((index - capacity(depth) : U32)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth))),sub_value(depth,index,limit,bound,choice)) :
    {U32.to_nat(index) == Nat.add(Shape.extent(depth),_) : Nat}
  %capacity_value(depth,child_limit_full(depth,limit)) : {U32.to_nat(index) == Nat.add(_,Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))) : Nat}
  Equal.sym(Nat,Nat.add(U32.to_nat(capacity(depth)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))),U32.to_nat(index),
    Equal.trans(Nat,Nat.add(U32.to_nat(capacity(depth)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))),
      Nat.add(Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth))),U32.to_nat(capacity(depth))),U32.to_nat(index),
      Order.commutative(U32.to_nat(capacity(depth)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))),Subtraction.restore(U32.to_nat(index),U32.to_nat(capacity(depth)),right_order(depth,index,choice))))

Uses (19):
  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.add
  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=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=commutative
  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=capacity_value
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_address_bounds.bend&name=child_limit_full
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_address_bounds.bend&name=right_order
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_address_bounds.bend&name=sub_value
  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_subtraction.bend&name=restore