Dip toes into creating end-to-end traces

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

Language/Properties.agda

@@ -7,6 +7,7 @@ open import Language.Traces
 
 open import Data.Fin as Fin using (zero)
 open import Data.List using (_∷_; [])
+open import Data.List.Relation.Unary.Any using (here)
 open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
 open import Data.Product using (Σ; _,_; _×_)
 open import Data.Vec.Properties using (lookup-++ˡ; ++-identityʳ; lookup-++ʳ)
@@ -84,4 +85,11 @@ Trace-loop g₁ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') =
 
 buildCfg-sufficient : ∀ {s : Stmt} {ρ₁ ρ₂ : Env} → ρ₁ , s ⇒ˢ ρ₂ →
                       EndToEndTrace {buildCfg s} ρ₁ ρ₂
-buildCfg-sufficient = {!!}
+buildCfg-sufficient (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs ρ₁,bs⇒ρ₂) =
+    record
+        { idx₁ = zero
+        ; idx₁∈inputs = here refl
+        ; idx₂ = zero
+        ; idx₂∈outputs = here refl
+        ; trace = Trace-single (ρ₁,bs⇒ρ₂ ∷ [])
+        }