Bisimilarity choice assoc
Cslib.CCS.bisimilarity_choice_assoc
Plain-language statement
P + (Q + R) ~ (P + Q) + R
Exact Lean statement
theorem bisimilarity_choice_assoc :
(choice p (choice q r)) ~[lts (defs := defs)] (choice (choice p q) r)Formal artifact
Lean source
theorem bisimilarity_choice_assoc : (choice p (choice q r)) ~[lts (defs := defs)] (choice (choice p q) r) := by use ChoiceAssoc, ChoiceAssoc.assoc intro s1 s2 hr μ apply And.intro <;> cases hr case left.assoc p q r => intro s htr refine ⟨s, ?_, ChoiceAssoc.id⟩ cases htr case choiceL htr => apply Tr.choiceL; apply Tr.choiceL; assumption case choiceR htr => cases htr case choiceL htr => apply Tr.choiceL; apply Tr.choiceR; assumption case choiceR htr => apply Tr.choiceR; assumption case right.assoc p q r => intro s htr refine ⟨s, ?_, ChoiceAssoc.id⟩ cases htr case choiceL htr => cases htr case choiceL htr => apply Tr.choiceL; assumption case choiceR htr => apply Tr.choiceR; apply Tr.choiceL; assumption case choiceR htr => apply Tr.choiceR; apply Tr.choiceR; assumption all_goals grind [ChoiceAssoc.id]- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Languages/CCS/BehaviouralTheory.lean:223-246
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
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.