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Project-declaredLean 4.31.0 · null

Find? notmem keys

Cedar.Data.Map.find?_notmem_keys

Plain-language statement

Inverse of find?_mem_toList, except that this requires wf

Exact Lean statement

public theorem find?_notmem_keys [LT α] [DecidableLT α] [StrictLT α] [DecidableEq α] {m : Map α β} {k : α}
  (wf : m.WellFormed) :
  m.find? k = none ↔ k ∉ m.keys

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
public theorem find?_notmem_keys [LT α] [DecidableLT α] [StrictLT α] [DecidableEq α] {m : Map α β} {k : α}  (wf : m.WellFormed) :  m.find? k = none  k  m.keys:= by  unfold find? at *  constructor <;> intro h₁  case mp =>    split at h₁ <;> simp at h₁    rename_i h₂    intro h₃    replace v, h₃ := in_keys_exists_value h₃    apply h₂ k v ; clear h₂    replace h₃ := (in_list_iff_find?_some wf).mp h₃    unfold find? at h₃    split at h₃ <;> simp only [Option.some.injEq, reduceCtorEq] at h₃    · subst v ; rename_i k' v h₂      simp only [h₂, Option.some.injEq, Prod.mk.injEq, and_true]      simpa using List.find?_some h₂  case mpr =>    split <;> simp ; rename_i k' v h₂    · apply h₁ ; clear h₁      have h₃ := List.find?_some h₂ ; simp at h₃ ; subst k'      replace h₂ := List.mem_of_find?_eq_some h₂      exact in_list_in_keys h₂
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Data/Map.lean:443-466

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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? 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.

View proof record