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Aperiodic completeness

Lax149335.AperiodicCompleteness · concepts/Lax149335/AperiodicCompleteness.lean · lax-149335

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    Natural Language Statement

    Corollary

    Corollary 7.6 (Aperiodic completeness). If aperiodic rational terms ff and gg have the same denotation, then f≡gf \equiv g.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
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    1import Lax149335.EquationalTheory
    2
    3/-!
    4---
    5title: Aperiodic completeness
    6type: corollary
    7---
    8**Corollary 7.6 (Aperiodic completeness).** If aperiodic rational terms ff and gg have
    9the same denotation, then f≡gf \equiv g.
    10-/
    11
    12namespace Lax149335.AperiodicCompleteness
    13
    14open Lax149335.Types Lax149335.Terms Lax149335.EquationalTheory
    15
    16/-- **Corollary 7.6.** Aperiodic terms with the same denotation are provably equivalent. -/
    17axiom completeness_aperiodic {A B : Ty} (f g : Term A B)
    18 (hf : IsAperiodic f) (hg : IsAperiodic g) (h : f.den = g.den) : f ≡ₜ g
    19
    20end Lax149335.AperiodicCompleteness
    21
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