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Project-declaredLean 4.31.0 · null

Map make append find disjoint

Cedar.Data.Map.map_make_append_find_disjoint'

Plain-language statement

A variant of map_make_append_find_disjoint.

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} {v : β}
  (hfind₁ : l₁.find? (λ ⟨k', _⟩ => k' == k) = none)
  (hfind₂ : l₂.find? (λ ⟨k', _⟩ => k' == k) = .some (k, v))
  (heq : ∀ x₁ x₂, x₁ ∈ l₂ → x₂ ∈ l₂ → x₁.fst = x₂.fst → x₁ = x₂) :
  (Map.make (l₁ ++ l₂)).find? k = some v

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} {v : β}  (hfind₁ : l₁.find? (λ k', _ => k' == k) = none)  (hfind₂ : l₂.find? (λ k', _ => k' == k) = .some (k, v))  (heq :  x₁ x₂, x₁  l₂  x₂  l₂  x₁.fst = x₂.fst  x₁ = x₂) :  (Map.make (l₁ ++ l₂)).find? k = some v:= by  have : (l₂.find? (λ k', _ => k' == k)).isSome  := by simp only [hfind₂, Option.isSome]  have v', hfind_k, hmem := map_make_append_find_disjoint hfind₁ this  have := List.mem_of_find?_eq_some hfind₂  have := heq _ _ this hmem  simp only [Prod.mk.injEq, true_and, forall_const] at this  simp only [this, hfind_k]
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Data/Map.lean:1714-1729

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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.

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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.

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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.

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