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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

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 t

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
@[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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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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