All proofs
Project-declaredLean 4.31.0 · null

Canonicalize id filter

List.canonicalize_id_filter

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 id

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
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

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