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Promote traces through loop

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-04-27 14:38:07 -07:00
parent 660f6594fd
commit f555947184
1 changed files with 6 additions and 0 deletions
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@ -75,3 +75,9 @@ Trace-↦ʳ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ (Graph.edges g₁ ↑ˡᵉ Graph.size g₂) Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ (Graph.edges g₁ ↑ˡᵉ Graph.size g₂)
(ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx))) (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx)))
(Trace-↦ʳ g₁ g₂ tr') (Trace-↦ʳ g₁ g₂ tr')
Trace-loop : ∀ (g₁ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ → Trace {loop g₁} idx₁ idx₂ ρ₁ ρ₂
Trace-loop g₁ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-single ρ₁⇒ρ₂
Trace-loop g₁ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') =
Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ idx₁→idx) (Trace-loop g₁ tr')