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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Derivable In cut away

Cslib.Logic.PL.DerivableIn.cut_away

computer sciencecomputabilityprogram semanticsbasic

Plain-language statement

Remove unnecessary hypotheses. This can't be computable because it requires picking an order on the finset Δ.

Exact Lean statement

theorem DerivableIn.cut_away {Γ Γ' : Ctx Atom} {B : Proposition Atom}
    (hΔ : ∀ A ∈ Γ', DerivableIn T (Γ ⊢ A)) (hDer : DerivableIn T ((Γ ∪ Γ') ⊢ B)) :
    DerivableIn T (Γ ⊢ B)

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem DerivableIn.cut_away {Γ Γ' : Ctx Atom} {B : Proposition Atom}    (hΔ : ∀ A ∈ Γ', DerivableIn T (Γ ⊢ A)) (hDer : DerivableIn T ((Γ ∪ Γ') ⊢ B)) :    DerivableIn T (Γ ⊢ B) := by  induction Γ' using Finset.induction with  | empty => exact DerivableIn.weakCtx (by grind) hDer  | insert A Δ hA ih =>    apply ih    · intro A' hA'      exact hΔ A' <| Finset.mem_insert_of_mem hA'    · apply Finset.union_left_idem Γ Δ ▸ DerivableIn.cut (Δ := Γ ∪ Δ)      · exact hΔ A <| Finset.mem_insert_self A Δ      · rwa [← Finset.union_insert A Γ Δ]
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Logics/Propositional/NaturalDeduction/Basic.lean:227-238

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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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