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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Standard to redex

Cslib.LambdaCalculus.LocallyNameless.Untyped.Term.Standard.to_redex

Plain-language statement

Standard reduction is contained in full β-reduction.

Exact Lean statement

lemma Standard.to_redex (step : M ⭢ₛ N) : M ↠βᶠ N

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
lemma Standard.to_redex (step : M ⭢ₛ N) : M ↠βᶠ N := by  induction step  case fvar => rfl  case app step_L step_M ih_L ih_M =>    exact .trans (redex_app_l_cong ih_L step_M.lc_l) (redex_app_r_cong ih_M step_L.lc_r)  case abs xs _ ih => exact FullBeta.redex_abs_cong xs ih  case rdx n m' _ lc_m lc_n cbn_m std_p ih =>    have step1 := redex_app_l_cong (CBN.to_redex cbn_m) lc_n    have step2 : m'.abs.app n ↠βᶠ m' ^ n := .single (.base (.beta (CBN.steps_lc_r lc_m cbn_m) lc_n))    exact .trans step1 (.trans step2 ih)
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StandardReduction.lean:132-141

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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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