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Project-declaredLean 4.31.0 · null

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.

Exact Lean statement

public theorem find?_ext [LT α] [DecidableLT α] [StrictLT α] [DecidableEq α] {m₁ m₂ : Map α β}
  (wf₁ : m₁.WellFormed)
  (wf₂ : m₂.WellFormed)
  (h : ∀ k, m₁.find? k = m₂.find? k) :
  m₁ = m₂

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
public theorem find?_ext [LT α] [DecidableLT α] [StrictLT α] [DecidableEq α] {m₁ m₂ : Map α β}  (wf₁ : m₁.WellFormed)  (wf₂ : m₂.WellFormed)  (h :  k, m₁.find? k = m₂.find? k) :  m₁ = m₂:= by  apply eq_iff_toList_equiv wf₁ wf₂ |>.mp  constructor  · intro k, v h₁    have h₂ := (in_list_iff_find?_some wf₁).mp h₁    rw [h] at h₂    exact (in_list_iff_find?_some wf₂).mpr h₂  · intro k, v h₁    have h₂ := (in_list_iff_find?_some wf₂).mp h₁    rw [ h] at h₂    exact (in_list_iff_find?_some wf₁).mpr h₂
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Data/Map.lean:471-486

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Related declarations

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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Project-declaredLean 4.31.0

In list iff find? some

Cedar.Data.Map.in_list_iff_find?_some

Plain-language statement

The mpr direction of this does not need the wf precondition and, in fact, is available separately as find?_mem_toList above

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

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