StorageRefinement.sequence_element: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/storage_refinement.bend as StorageRefinement
Lines 262-282 of stelliferous@0.0.2.0/proofs/storage_refinement.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/storage_refinement.bend&start_line=262&end_line=282

import Base
import stelliferous@0.0.2.0/proofs/storage_tree_model.bend as Tree
import stelliferous@0.0.2.0/proofs/loop_projection.bend as Projection
import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as Arithmetic
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

# An observed logical prefix has the actual stored element at every valid index.
# Capacity need not equal count; address overflow remains explicitly modular.
def sequence_element(~Element: Data,+count: Nat,+offset: U32,+tree: Tree.Tree<Element>,+index: Nat,
  inside: {Nat.is_lt(index,count) == True{} : Bool}) ->
  {List.get(&2,Element,Tree.read_sequence(~Element,count,offset,tree),index) ==
    Some{Tree.read(Element,tree,(offset + U32.from_nat(index) : U32))} : Maybe<&2,Element>}:
  match count index:
    case 0n 0n:
      Empty.absurd({None{} == Some{Tree.read(Element,tree,(offset + 0 : U32))} : Maybe<&2,Element>},WordEncoding.false_true(inside))
    case 0n 1n+previous:
      Empty.absurd({None{} == Some{Tree.read(Element,tree,(offset + U32.from_nat(1n+previous) : U32))} : Maybe<&2,Element>},WordEncoding.false_true(inside))
    case 1n+rest 0n:
      %Equal.sym(U32,(offset + 0 : U32),offset,Arithmetic.add_zero(offset)) :
        {Some{Tree.read(Element,tree,offset)} == Some{Tree.read(Element,tree,_)} : Maybe<&2,Element>}
      {==}
    case 1n+ +rest 1n+ +previous:
      %Equal.sym(U32,(offset + U32.from_nat(1n+previous) : U32),((offset + 1 : U32) + U32.from_nat(previous) : U32),
        Projection.indexed_successor(offset,previous)) :
        {List.get(&2,Element,Tree.read_sequence(~Element,rest,(offset + 1 : U32),tree),previous) ==
          Some{Tree.read(Element,tree,_)} : Maybe<&2,Element>}
      sequence_element(~Element,rest,(offset + 1 : U32),tree,previous,inside)

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=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/loop_projection.bend&name=indexed_successor
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_tree_model.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_tree_model.bend&name=read
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/storage_tree_model.bend&name=read_sequence
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true