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Project-declaredLean 4.31.0 · null

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

Exact Lean statement

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

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
public theorem find?_some_iff_in_values [LT α] [DecidableLT α] [StrictLT α] [DecidableEq α] {m : Map α β} {v : β}  (wf : m.WellFormed) :  ( k, m.find? k = .some v)  v  m.values:= by  constructor  case mp =>    intro k, h₁    exact find?_some_implies_in_values h₁  case mpr =>    simp only [values, List.mem_map]    intro h₁    replace ⟨⟨k, v', h₁, h₂⟩⟩ := h₁    simp only at h₂    subst v'    exists k    simp [h₁,  in_list_iff_find?_some wf]
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Data/Map.lean:1001-1016

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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

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