All proofs
Project-declaredLean 4.31.0 · null

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

Exact Lean statement

public theorem in_list_iff_find?_some [DecidableEq α] [LT α] [DecidableLT α] [StrictLT α] {k : α} {v : β} {m : Map α β}
  (wf : m.WellFormed) :
  (k, v) ∈ m.toList ↔ m.find? k = some v

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
public theorem in_list_iff_find?_some [DecidableEq α] [LT α] [DecidableLT α] [StrictLT α] {k : α} {v : β} {m : Map α β}  (wf : m.WellFormed) :  (k, v)  m.toList  m.find? k = some v:= by  unfold find?  constructor  case mp =>    intro h₁    cases h₂ : m.toList.find? λ x => match x with | (k', _) => k' == k    case none =>      exfalso      rw [List.find?_eq_none] at h₂      apply h₂ (k, v) h₁ ; clear h₂      simp only [beq_self_eq_true]    case some kv =>      simp only [Option.some.injEq]      have h₃ := List.find?_some h₂      simp only [beq_iff_eq] at h₃      subst h₃      replace h₃ := List.mem_of_find?_eq_some h₂      apply (key_maps_to_one_value kv.fst v kv.snd m wf h₁ _).symm      trivial  case mpr => exact find?_mem_toList
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Data/Map.lean:418-440

Reuse this declaration

Bring the exact result into your workflow

The import identifies the source module. Your project still needs the pinned package dependency shown on this page.

What this badge means

This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.

Continue in this project

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.

View proof record
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.

View proof record
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.

View proof record