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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Saturate m Tr s MTr not nil iff

Cslib.LTS.saturate_mTr_sMTr_not_nil_iff

Plain-language statement

A saturated multistep transition with a nonempty label list implies a multistep transition.

Exact Lean statement

@[scoped grind =]
theorem saturate_mTr_sMTr_not_nil_iff [HasTau Label] {lts : LTS State Label}
    (hμs : μs ≠ []) : lts.saturate.MTr s μs s' ↔ lts.SMTr s μs s'

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
@[scoped grind =]theorem saturate_mTr_sMTr_not_nil_iff [HasTau Label] {lts : LTS State Label}    (hμs : μs  []) : lts.saturate.MTr s μs s'  lts.SMTr s μs s' := by  induction μs generalizing s  case nil => contradiction  case cons x xs ih =>    apply Iff.intro <;> intro h    case mp =>      cases h      case stepL sb htr hmtr =>        cases xs with        | nil =>          cases hmtr          apply LTS.SMTr.stepL htr (by grind only [SMTr.fromMTr, MTr.refl])        | cons x' xs' =>          exact LTS.SMTr.stepL htr ((ih (by simp)).mp hmtr)    case mpr =>      cases h      case stepL sb htr hmtr =>        cases xs with        | nil =>          cases hmtr          case τ h_τ =>            exact LTS.MTr.stepL              (LTS.STr.comp LTS.STr.refl htr h_τ)              LTS.MTr.refl        | cons x' xs' =>          exact LTS.MTr.stepL htr ((ih (by simp)).mpr hmtr)
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Foundations/Semantics/LTS/HasTau.lean:201-228

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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

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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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