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Proved part of the braiding coherence lB=r #67

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MirceaS
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@MirceaS MirceaS commented Oct 23, 2019

Proved the -⊗1 version of the coherence theorem.
I might get around to proving the final identity later but for now I thought it would be useful to have this as a PR and other people can do it in the meantime if they want.
Also, I wasn't sure where exactly to write it so I created a new module inside Braided.agda. Feel free to move stuff around if that is not appropriate.

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MirceaS commented Oct 23, 2019

TODO: Open the module publicly exposing the final identity once it's proved

@@ -51,3 +57,38 @@ record Braided : Set (levelOfTerm M) where
B ⇒⟨ Z ⊗₀ X ⊗₀ Y ⟩
associator.to

module Properties where
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I would define this in a separate module in a new file.

@@ -41,9 +41,12 @@ module Basic where
open Basic public

module Utils where
assoc² : ((i ∘ h) ∘ g) ∘ f ≈ i ∘ (h ∘ (g ∘ f))
assoc² : ((i ∘ h) ∘ g) ∘ f ≈ i ∘ h ∘ g ∘ f
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I'm not sure this should be changed. I actually like the more explicit version with parentheses better.

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