Standard subst
Cslib.LambdaCalculus.LocallyNameless.Untyped.Term.Standard.subst
Plain-language statement
Standard reduction is preserved by substitution.
Exact Lean statement
lemma Standard.subst (hM : M ⭢ₛ M') (hN : N ⭢ₛ N') (x : Var) (lc_N : LC N) (lc_N' : LC N') :
(M[x := N]) ⭢ₛ (M'[x := N'])Formal artifact
Lean source
lemma Standard.subst (hM : M ⭢ₛ M') (hN : N ⭢ₛ N') (x : Var) (lc_N : LC N) (lc_N' : LC N') : (M[x := N]) ⭢ₛ (M'[x := N']) := by induction hM generalizing N N' case fvar => simp only [Term.subst_fvar] split · exact hN · exact fvar _ case app ihL ihM => exact app (ihL hN lc_N lc_N') (ihM hN lc_N lc_N') case abs m m' _ _ ih => apply abs <| free_union [fv] Var grind case rdx n m' _ lc_m lc_n cbn_m std_p ih => rw [Term.subst_app] have std_p_subst := ih hN lc_N lc_N' rw [Term.subst_open x N n m' lc_N] at std_p_subst exact rdx (subst_lc lc_m lc_N) (subst_lc lc_n lc_N) (CBN.steps_subst x cbn_m lc_N) std_p_subst- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StandardReduction.lean:97-113
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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.
Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family cover
Cslib.Automata.NA.Buchi.buchiFamily_cover
Project documentation
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Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family saturation
Cslib.Automata.NA.Buchi.buchiFamily_saturation
Plain-language statement
na.buchiFamily saturates the ω-language accepted by na.
Source project: Lean Computer Science Library
Person-level attribution pending.