Slice contains reachable
Cedar.Thm.slice_contains_reachable
Project documentation
If an entity is reachable in n steps, then it must be included in slice at n. This lemma talks about the inner slicing function, so it's possible that the entity isn't in the original entities if it's in work.
Exact Lean statement
theorem slice_contains_reachable {n: Nat} {work : Set EntityUID} {euid : EntityUID} {entities : Entities}
(hw : ReachableIn entities work euid (n + 1)) :
euid ∈ Entities.sliceAtLevel.sliceAtLevel entities work (n + 1)Formal artifact
Lean source
theorem slice_contains_reachable {n: Nat} {work : Set EntityUID} {euid : EntityUID} {entities : Entities} (hw : ReachableIn entities work euid (n + 1)) : euid ∈ Entities.sliceAtLevel.sliceAtLevel entities work (n + 1):= by cases hw case in_start hw => exact in_work_then_in_slice hw case step ed euid' hf hi hw => simp only [Entities.sliceAtLevel.sliceAtLevel] let slice' := (work.elts.filterMap (Map.find? entities)).mapUnion λ ed => Entities.sliceAtLevel.sliceAtLevel entities ed.sliceEUIDs n rw [Set.mem_union] right cases n case _ => cases hw case _ n' => simp only [List.mem_mapUnion_iff_mem_exists, List.mem_filterMap] exists ed and_intros · exists euid' · exact slice_contains_reachable hw- Project
- Cedar Specification
- License
- Apache-2.0
- Commit
- 3f093947b8ae
- Source
- cedar-lean/Cedar/Thm/Validation/Slice/Reachable.lean:236-255
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
Related declarations
Find? ext
Cedar.Data.Map.find?_ext
Plain-language statement
Two well-formed maps are equal if they have the same find? for every key.
Source project: Cedar Specification
Person-level attribution pending.
Find? notmem keys
Cedar.Data.Map.find?_notmem_keys
Plain-language statement
Inverse of find?_mem_toList, except that this requires wf
Source project: Cedar Specification
Person-level attribution pending.
Find? some iff in values
Cedar.Data.Map.find?_some_iff_in_values
Plain-language statement
The mp direction of this does not need the wf precondition and, in fact, is available separately as find?_some_implies_in_values above
Source project: Cedar Specification
Person-level attribution pending.