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 vFormal artifact
Lean source
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
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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.