Totalize nonsink mtr iff
Cslib.LTS.totalize.nonsink_mtr_iff
Plain-language statement
In totalize, the multistep transitions between non-sink states correspond exactly to the multistep transitions in the original LTS.
Exact Lean statement
@[simp]
theorem totalize.nonsink_mtr_iff {μs : List Label} {s t : State} :
lts.totalize.MTr (some s) μs (some t) ↔ lts.MTr s μs tFormal artifact
Lean source
@[simp]theorem totalize.nonsink_mtr_iff {μs : List Label} {s t : State} : lts.totalize.MTr (some s) μs (some t) ↔ lts.MTr s μs t := by constructor <;> intro h · generalize h_s : (some s : Option State) = s' generalize h_t : (some t : Option State) = t' rw [h_s, h_t] at h induction h generalizing s case refl _ => grind [MTr] case stepL t1' μ t2' μs t3' h_tr h_mtr h_ind => obtain ⟨rfl⟩ := h_s cases t2' case some t2 => grind [MTr, totalize.nonsink_tr_iff.mp h_tr] case none => grind [totalize.no_sink_to_nonsink] · induction h case refl _ => grind [MTr] case stepL t1 μ t2 μs t3 h_tr h_mtr h_ind => grind [MTr, totalize.nonsink_tr_iff.mpr h_tr]- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Foundations/Semantics/LTS/Total.lean:98-115
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Plain-language statement
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Person-level attribution pending.
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Cslib.Automata.NA.Buchi.buchiFamily_cover
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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.