TraversalCertificate.operation_equation: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/traversal_certificate.bend as TraversalCertificate
Lines 70-83 of stelliferous@0.0.2.0/proofs/traversal_certificate.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/traversal_certificate.bend&start_line=70&end_line=83

import Base
import stelliferous@0.0.2.0/proofs/storage_tree_model.bend as Tree
import stelliferous@0.0.2.0/proofs/storage_certificate.bend as Certificate
import stelliferous@0.0.2.0/proofs/traversal_witness.bend as TraversalWitness

def operation_equation(~Reader: Type,~Element: Data,~Metadata: Data,~ReaderCertificate: @-reader: Reader -> Data,
  ~operation: Metadata -> Reader -> Array<Element> -> Reader & Array<Element>,
  ~preserves: @+depth: Nat -> @metadata: Metadata -> @-reader: Reader -> @-output: Array<Element> -> ReaderCertificate(reader) ->
    {output == Tree.pack(Element,Certificate.normalized(Element,depth,Tree.reflect(Element,output))) : Array<Element>} ->
    TraversalWitness.ResultEvidence<Reader,Element,reader,depth,operation(metadata,reader,output)>,
  metadata: Metadata,-reader: Reader,-output: Array<Element>,reader_certificate: ReaderCertificate(reader),+depth: Nat,
  equation: {output == Tree.pack(Element,Certificate.normalized(Element,depth,Tree.reflect(Element,output))) : Array<Element>}) ->
  {TraversalWitness.second(~Reader,~Array<Element>,operation(metadata,reader,output)) ==
    Tree.pack(Element,Certificate.normalized(Element,depth,Tree.reflect(Element,TraversalWitness.second(~Reader,~Array<Element>,operation(metadata,reader,output))))) : Array<Element>}:
  %Certificate.restored(Element,depth,TraversalWitness.second(~Reader,~Array<Element>,operation(metadata,reader,output)),
    TraversalWitness.output_witness(~Reader,~Element,reader,depth,operation(metadata,reader,output),
      preserves(depth,metadata,reader,output,reader_certificate,equation))) :
    {_ == Tree.pack(Element,Certificate.normalized(Element,depth,Tree.reflect(Element,TraversalWitness.second(~Reader,~Array<Element>,operation(metadata,reader,output))))) : Array<Element>}
  {==}

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_certificate.bend&name=normalized
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_certificate.bend&name=restored
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_tree_model.bend&name=pack
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_tree_model.bend&name=reflect
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/traversal_witness.bend&name=ResultEvidence
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/traversal_witness.bend&name=output_witness
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/traversal_witness.bend&name=second