Tr diamond
Cslib.FLP.Algorithm.tr_diamond
Plain-language statement
A diamond property for the transition relation a.lts.Tr.
Exact Lean statement
theorem tr_diamond {ps : Set P} {x1 x2 : Action P M} {s s1 s2 : State P M S}
(hx1 : DestIn ps x1) (hs1 : a.lts.Tr s x1 s1)
(hx2 : DestIn psᶜ x2) (hs2 : a.lts.Tr s x2 s2) :
∃ s', a.lts.Tr s1 x2 s' ∧ a.lts.Tr s2 x1 s'Formal artifact
Lean source
theorem tr_diamond {ps : Set P} {x1 x2 : Action P M} {s s1 s2 : State P M S} (hx1 : DestIn ps x1) (hs1 : a.lts.Tr s x1 s1) (hx2 : DestIn psᶜ x2) (hs2 : a.lts.Tr s x2 s2) : ∃ s', a.lts.Tr s1 x2 s' ∧ a.lts.Tr s2 x1 s' := by cases x1 <;> cases x2 · grind [Algorithm.lts] · grind [Algorithm.lts] · grind [Algorithm.lts] · case some m1 m2 => have hd : m1.dest ≠ m2.dest := by grind [DestIn] obtain ⟨h_m1, rfl⟩ := hs1 obtain ⟨h_m2, rfl⟩ := hs2 simp only [Algorithm.lts, exists_eq_right_right] grind [recvMsg_comm (a := a) hd h_m1 h_m2]- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Computability/Distributed/FLP/Algorithm.lean:201-214
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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.