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
@[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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Plain-language statement
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Person-level attribution pending.
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Source project: Lean Computer Science Library
Person-level attribution pending.
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Cslib.Automata.NA.Buchi.buchiFamily_saturation
Plain-language statement
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Source project: Lean Computer Science Library
Person-level attribution pending.