Codyroux/compactness #123
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Codyroux/compactness #123
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This was referenced Sep 30, 2024
| infix:50 " ⊧ " => (models) | ||
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| infix:50 " ⊢ " => (derive) | ||
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Maybe the definitions up to this point can ultimately end up in their own file, called something like Satisfaction.lean? I suggest this because I expect lots of other files (like my Duality.lean in progress) will need to use these definitions, but may not need everything in Completeness.lean.
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I agree! I'd like to get this merged first, if that's all right, I'm getting nervous about all the rebasing.
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Yay. I'll go in and fix the blueprint stuff later. |
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I agree, I'll either do it here, or in a further PR.
…On Mon, Sep 30, 2024, 1:54 AM Franklin Pezzuti Dyer < ***@***.***> wrote:
***@***.**** commented on this pull request.
------------------------------
In equational_theories/Completeness.lean
<#123 (comment)>
:
> +
+def satisfiesSet {α : Type} (G : Type) [Magma G] (Γ : Set (MagmaLaw α)) : Prop :=
+ ∀ E ∈ Γ, satisfies G E
+
+
+def models {α} (Γ : Ctx α) (E : MagmaLaw α) : Prop :=
+ ∀ (G : Type)[Magma G], satisfiesSet G Γ → satisfies G E
+
+infix:50 " ⊧ " => (satisfies)
+
+infix:50 " ⊧ " => (satisfiesSet)
+
+infix:50 " ⊧ " => (models)
+
+infix:50 " ⊢ " => (derive)
+
Maybe the definitions up to this point can ultimately end up in their own
file, called something like Satisfaction.lean? I suggest this because I
expect lots of other files (like my Duality.lean in progress) will need
to use these definitions, but may not need everything in Completeness.lean
.
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.
You are receiving this because you authored the thread.Message ID:
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For now just soundness.
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* feat: add preorder on magma laws This builds on the `MagmaLaw` structure defined in #113 and thus depends on it. * integrate with definitions from #123 * add equivalence suggested by @codyroux * remove whitespace * add suggestions from @madvorak * more style changes suggested by @madvorak * minor improvements --------- Co-authored-by: Pietro Monticone <38562595+pitmonticone@users.noreply.github.com>
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closes #104
Closes #104