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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Saturate tr saturate s Tr

Cslib.LTS.saturate_tr_saturate_sTr

Plain-language statement

In a saturated LTS, the transition and saturated transition relations are the same.

Exact Lean statement

theorem saturate_tr_saturate_sTr [hHasTau : HasTau Label] (lts : LTS State Label)
    (hμ : μ = hHasTau.τ) : lts.saturate.Tr s μ = lts.saturate.STr s μ

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem saturate_tr_saturate_sTr [hHasTau : HasTau Label] (lts : LTS State Label)    (hμ : μ = hHasTau.τ) : lts.saturate.Tr s μ = lts.saturate.STr s μ := by  ext s'  apply Iff.intro <;> intro h  case mp =>    cases h    case refl => constructor    case tr hstr1 htr hstr2 =>      apply STr.single      exact STr.tr hstr1 htr hstr2  case mpr =>    cases h    case refl => constructor    case tr hstr1 htr hstr2 =>      rw [saturate_τsTr_τSTr_iff lts] at hstr1 hstr2      rw [sTr_τSTr_iff lts] at hstr1 hstr2      exact STr.comp hstr1 htr hstr2
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Foundations/Semantics/LTS/HasTau.lean:118-134

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Related declarations

Project-declaredLean 4.33.0-rc1

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.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

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.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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