All proofs
Project-declaredLean 4.31.0 · null

Map make append find disjoint

Cedar.Data.Map.map_make_append_find_disjoint

Plain-language statement

If a key exists in l₂ but not in l₁, then Map.make (l₁ ++ l₂) contains that key.

Exact Lean statement

public theorem map_make_append_find_disjoint
  [LT α] [StrictLT α] [DecidableEq α] [DecidableLT α]
  [SizeOf α] [SizeOf β]
  {l₁ : List (α × β)} {l₂ : List (α × β)} {k : α}
  (hfind₁ : l₁.find? (λ ⟨k', _⟩ => k' == k) = none)
  (hfind₂ : (l₂.find? (λ ⟨k', _⟩ => k' == k)).isSome) :
  ∃ v,
    (Map.make (l₁ ++ l₂)).find? k = some v ∧
    (k, v) ∈ l₂

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
public theorem map_make_append_find_disjoint  [LT α] [StrictLT α] [DecidableEq α] [DecidableLT α]  [SizeOf α] [SizeOf β]  {l₁ : List (α × β)} {l₂ : List (α × β)} {k : α}  (hfind₁ : l₁.find? (λ k', _ => k' == k) = none)  (hfind₂ : (l₂.find? (λ k', _ => k' == k)).isSome) :   v,    (Map.make (l₁ ++ l₂)).find? k = some v     (k, v)  l₂:= by  have hwf : (Map.make (l₁ ++ l₂)).WellFormed := by    exact Map.make_wf _  have hsub :    (Map.make (l₁ ++ l₂)).toList  l₁ ++ l₂  := by    apply List.canonicalize_subseteq  simp [Subset, List.Subset] at hsub  have v, hv :     v, (Map.make (l₁ ++ l₂)).find? k = some v  := by    simp only [Option.isSome] at hfind₂    split at hfind₂    rotate_left    contradiction    rename_i kv hkv    exists kv.snd    rw [make_find?_eq_list_find?]    rw [List.find?_append]    rw [hkv, hfind₁]    simp  simp only [hv, Option.some.injEq, exists_eq_left']  have := Map.find?_mem_toList hv  have := hsub k v this  cases this with  | inl hmem₁ =>    have := List.find?_eq_none.mp hfind₁    specialize this (k, v) hmem₁    simp at this  | inr h => exact h
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Data/Map.lean:1590-1628

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