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.valuesFormal artifact
Lean source
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
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.
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
Source project: Cedar Specification
Person-level attribution pending.