Bisimilarity par assoc
Cslib.CCS.bisimilarity_par_assoc
Plain-language statement
P | (Q | R) ~ (P | Q) | R
Exact Lean statement
theorem bisimilarity_par_assoc :
(par p (par q r)) ~[lts (defs := defs)] (par (par p q) r)Formal artifact
Lean source
theorem bisimilarity_par_assoc : (par p (par q r)) ~[lts (defs := defs)] (par (par p q) r) := by use ParAssoc, ParAssoc.assoc intro s1 s2 hr μ apply And.intro <;> cases hr case right.assoc => intro s2' htr unfold lts at * cases htr case parL p q r p' htr => cases htr case parL p q r p' _ => exists p'.par (q.par r) grind case parR p q r q' _ => exists p.par (q'.par r) grind case com μ p' μ' q' _ htrp htrq => exists p'.par (q'.par r) grind case parR p q r r' htr => exists p.par (q.par r') grind case com p q r μ p' μ' r' _ htr htr' => cases htr case parL p' _ => use p'.par (q.par r') grind case parR q' _ => use p.par (q'.par r') grind case com => grind case left.assoc => intro s2' htr unfold lts at * cases htr case parR htr => cases htr case parL p q r q' _ => exists (p.par q').par r grind case parR p q r r' _ => exists (p.par q).par r' grind case com p q r μ q' μ' r' _ htrp htrq => use (p.par q').par r' grind case parL p q r p' htr => exists (p'.par q).par r grind case com p q r μ p' μ' q' _ htr htr' => cases htr' case parL q' _ => use (p'.par q').par r grind case parR r' _ => use (p'.par q).par r' grind case com => grind all_goals grind- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Languages/CCS/BehaviouralTheory.lean:86-145
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Related declarations
Unique minimal
Cslib.Automata.DA.FinAcc.unique_minimal
Plain-language statement
The minimal DFA M accepting the language l is unique up to unique isomorphism.
Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family cover
Cslib.Automata.NA.Buchi.buchiFamily_cover
Project documentation
na.buchiFamily is a cover if na has only finitely many states. This theorem uses the Ramsey theorem for infinite graphs and does not depend on any details of na.BuchiCongruence other than that it is of finite index.
Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family saturation
Cslib.Automata.NA.Buchi.buchiFamily_saturation
Plain-language statement
na.buchiFamily saturates the ω-language accepted by na.
Source project: Lean Computer Science Library
Person-level attribution pending.