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
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
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.
Source project: Cedar Specification
Person-level attribution pending.
Find? notmem keys
Cedar.Data.Map.find?_notmem_keys
Plain-language statement
Inverse of find?_mem_toList, except that this requires wf
Source project: Cedar Specification
Person-level attribution pending.
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
Source project: Cedar Specification
Person-level attribution pending.