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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Is Weak Bisimulation iff is SWBisimulation

Cslib.LTS.isWeakBisimulation_iff_isSWBisimulation

computer sciencecomputabilityprogram semanticsbisimulation

Project documentation

We can now prove that any relation is a WeakBisimulation iff it is an SWBisimulation. This formalises lemma 4.2.10 in [Sangiorgi2011].

Exact Lean statement

theorem isWeakBisimulation_iff_isSWBisimulation
    [HasTau Label] {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} :
    IsWeakBisimulation lts₁ lts₂ r ↔ IsSWBisimulation lts₁ lts₂ r

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem isWeakBisimulation_iff_isSWBisimulation    [HasTau Label] {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} :    IsWeakBisimulation lts₁ lts₂ r ↔ IsSWBisimulation lts₁ lts₂ r := by  apply Iff.intro  case mp =>    intro h    rw [IsSWBisimulation.iff_isSimulation]    exact ⟨h.isSimulation.mono lts₁.tr_le_tr_saturate le_rfl,      h.inv.isSimulation.mono lts₂.tr_le_tr_saturate le_rfl⟩  case mpr =>    intro h    rw [IsWeakBisimulation, IsBisimulation.isSimulation_iff]    exact ⟨h.isSimulation.isSimulation_saturate_left,      h.isSimulation_flip.isSimulation_saturate_left⟩
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Foundations/Semantics/LTS/Bisimulation.lean:505-518

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Related declarations

Project-declaredLean 4.33.0-rc1

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Plain-language statement

The minimal DFA M accepting the language l is unique up to unique isomorphism.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

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Cslib.Automata.NA.Buchi.buchiFamily_cover

Project documentation

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computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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