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Finite axiomatisation

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

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    Natural Language Statement

    Theorem

    Theorem 4.1 (Finite axiomatisation). Two rational terms f,g:A→Bf, g : A \to B have the same denotation if and only if f≡gf \equiv g can be proved using Axioms 1–16.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    1import Lax149335.EquationalTheory
    2
    3/-!
    4---
    5title: Finite axiomatisation
    6type: theorem
    7---
    8**Theorem 4.1 (Finite axiomatisation).** Two rational terms f,g:A→Bf, g : A \to B have the same
    9denotation if and only if f≡gf \equiv g can be proved using Axioms 1–16.
    10-/
    11
    12namespace Lax149335.FiniteAxiomatisation
    13
    14open Lax149335.Types Lax149335.Terms Lax149335.EquationalTheory
    15
    16/-- **Theorem 4.1.** Two rational terms have the same denotation if and only if they are
    17provably equivalent. -/
    18axiom finite_axiomatisation {A B : Ty} (f g : Term A B) : f.den = g.den ↔ f ≡ₜ g
    19
    20end Lax149335.FiniteAxiomatisation
    21
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