Plain-language statement
Illustration that equiv_implies_canonical_eq does not hold for all functions f -- in particular, does not hold for Prod.fst. (One canonicalize produces [(1, false)], and the other produces [(1, true)].) -/ example : xs = [(1, false), (1, true)] → ys = [(1, true), (1, false)] → xs ≡ ys ∧ (canonicalize Prod.fst xs) ≠ (canonicalize Prod.fst ys) :...
Exact Lean statement
public theorem canonicalize_id_filter {α} [LT α] [StrictLT α] [DecidableLT α] (p : α → Bool) (xs : List α) :
(canonicalize id xs).filter p = (xs.filter p).canonicalize idFormal artifact
Lean source
public theorem canonicalize_id_filter {α} [LT α] [StrictLT α] [DecidableLT α] (p : α → Bool) (xs : List α) : (canonicalize id xs).filter p = (xs.filter p).canonicalize id:= by have h₁ : (canonicalize id xs).filter p ≡ xs.filter p := by apply filter_equiv apply Equiv.symm apply canonicalize_equiv have h₂ := canonicalize_equiv (filter p xs) exact sortedBy_equiv_implies_eq id (filter_sortedBy p (canonicalize_sortedBy id xs)) (canonicalize_sortedBy id (filter p xs)) (Equiv.trans h₁ h₂)- Project
- Cedar Specification
- License
- Apache-2.0
- Commit
- 3f093947b8ae
- Source
- cedar-lean/Cedar/Thm/Data/List/Canonical.lean:493-504
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
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.