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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Is Church injective

Cslib.SKI.isChurch_injective

computer sciencecomputabilityprogram semanticsevaluation

Plain-language statement

Injectivity for Church numerals

Exact Lean statement

theorem isChurch_injective (x y : SKI) (n m : Nat) (hx : IsChurch n x) (hy : IsChurch m y)
    (hxy : MJoin Red x y) : n = m

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem isChurch_injective (x y : SKI) (n m : Nat) (hx : IsChurch n x) (hy : IsChurch m y)    (hxy : MJoin Red x y) : n = m := by  suffices MJoin Red (churchK n) (churchK m) by    apply churchK_injective    exact eq_of_mJoin_red_redexFree this (churchK_redexFree n) (churchK_redexFree m)  apply mJoin_red_equivalence.trans (y := x ⬝ K ⬝ K)  · simp_rw [churchK_church]    exact mJoin_red_equivalence.symm <| Relation.MJoin.single (hx K K)  · apply mJoin_red_equivalence.trans (y := y ⬝ K ⬝ K)    · apply mJoin_red_head; apply mJoin_red_head; assumption    · simp_rw [churchK_church]      exact Relation.MJoin.single (hy K K)
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Languages/CombinatoryLogic/Evaluation.lean:250-261

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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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