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Project-declaredLean 4.31.0 · null

Map make filter Map find?

Cedar.Thm.map_make_filterMap_find?

Plain-language statement

For simplifying Factory.app on a UDF with a table of the form make (m.toList.filterMap f).

Exact Lean statement

theorem map_make_filterMap_find?
  [BEq α] [LawfulBEq α]
  [DecidableEq γ] [LT γ] [DecidableLT γ] [StrictLT γ]
  {m : Map α β}
  {k : α} {v : β} {k' : γ} {v' : κ}
  {f : α × β → Option (γ × κ)}
  (hfind : m.find? k = .some v)
  (hkv : f (k, v) = .some (k', v'))
  (hf : ∀ kv, (∃ v'', f kv = .some (k', v'')) → kv.1 = k) :
  (Map.make (m.toList.filterMap f)).find? k' = .some v'

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem map_make_filterMap_find?  [BEq α] [LawfulBEq α]  [DecidableEq γ] [LT γ] [DecidableLT γ] [StrictLT γ]  {m : Map α β}  {k : α} {v : β} {k' : γ} {v' : κ}  {f : α × β  Option (γ × κ)}  (hfind : m.find? k = .some v)  (hkv : f (k, v) = .some (k', v'))  (hf :  kv, ( v'', f kv = .some (k', v''))  kv.1 = k) :  (Map.make (m.toList.filterMap f)).find? k' = .some v':= by  rw [ Map.list_find?_iff_make_find?]  simp only [List.find?_filterMap]  have :    List.find? (fun a => Option.any (fun x => x.fst == k') (f a)) m.toList    = .some (k, v)  := by    apply Map.map_find?_implies_find?_weaker_pred hfind    · intros kv h      simp only [Option.any] at h      split at h      · rename_i f_out heq        simp at h        apply hf kv        exists f_out.snd        simp only [heq, h]      · contradiction    · simp [        Option.any,        hkv,      ]  simp [this, hkv]
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/SymCC/Term/UDF.lean:31-62

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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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