All proofs
Project-declaredLean 4.31.0 · null

Extract? implies enum complete

Cedar.Thm.extract?_implies_enum_complete

Plain-language statement

SymEnv.extract? always produces a concrete Env that satisfies Env.EnumCompleteFor.

Exact Lean statement

theorem extract?_implies_enum_complete
  {env : Env} {εnv : SymEnv} {I : Interpretation} {exprs : List Expr}
  (hext : env = εnv.extract? exprs I) :
  Env.EnumCompleteFor env εnv

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem extract?_implies_enum_complete  {env : Env} {εnv : SymEnv} {I : Interpretation} {exprs : List Expr}  (hext : env = εnv.extract? exprs I) :  Env.EnumCompleteFor env εnv:= by  simp only [    SymEnv.extract?, SymEnv.concretize?,    bind, Option.bind,  ] at hext  split at hext  contradiction  rename_i req hreq  simp only at hext  split at hext  contradiction  rename_i entities hents  simp only [Option.some.injEq] at hext  simp only [hext, Env.EnumCompleteFor]  intros uid δ eids hfind_uid_ty heids heid  have huid := sym_entities_entityUIDs_include_enums (Interpretation.repair (footprints exprs εnv) εnv I) hfind_uid_ty heids heid  replace eds, heds, hents := concretize?_εs_some_eq hents  simp only [hents]  have ⟨⟨uid', data, hmem_uid'_data, huid'  := List.mapM_some_implies_all_some heds uid    ((Set.mem_union _ _ uid).mpr (Or.intro_right _ huid))  have δ, d, hfind_uid_ty, hd, heq_uid' := concretize?_entityData?_some_eq huid'  simp only [Prod.mk.injEq] at heq_uid'  simp only [heq_uid'.1] at hmem_uid'_data huid'  exists data  rw [ Map.list_find?_iff_make_find?]  apply List.find?_unique_entry  · intros x hmem heq_fst    have uid', data' := x    simp only [beq_iff_eq] at heq_fst    simp only [heq_fst]    have uid'', hmem_uid'', huid'' := List.mapM_some_implies_all_from_some heds (uid', data') hmem    have _, d', hfind_uid_ty', hd', heq_uid'' := concretize?_entityData?_some_eq huid''    simp only [Prod.mk.injEq] at heq_uid''    simp only [heq_uid''.1, heq_fst] at hd' hfind_uid_ty'    simp only [hfind_uid_ty, Option.some.injEq] at hfind_uid_ty'    simp only [hfind_uid_ty'] at hd'    simp only [hd', Option.some.injEq] at hd    simp only [heq_uid''.2, hd, heq_uid'.2]  · exact hmem_uid'_data  · simp
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/SymCC/Enforcer/Extractor.lean:503-547

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

Project-declaredLean 4.31.0

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.

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

View proof record
Project-declaredLean 4.31.0

Find? notmem keys

Cedar.Data.Map.find?_notmem_keys

Plain-language statement

Inverse of find?_mem_toList, except that this requires wf

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

View proof record
Project-declaredLean 4.31.0

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

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

View proof record