induction e <;> simp [rcns]
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
e : s₁ ↓ᵢ+ s₂
⊢ s₂.progress = s₁.progress ∪ {a | a ∈ rcns e}
case single
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ : State α
a✝ : s₁✝ ↓ᵢ s₂✝
⊢ s₂✝.progress = insert (Execution.Instantaneous.Step.rcn a✝) s₁✝.progress

case trans
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ s₃✝ : State α
a✝¹ : s₁✝ ↓ᵢ s₂✝
a✝ : s₂✝ ↓ᵢ+ s₃✝
a_ih✝ : s₃✝.progress = s₂✝.progress ∪ {a | a ∈ rcns a✝}
⊢ s₃✝.progress = s₁✝.progress ∪ {a | a = Execution.Instantaneous.Step.rcn a✝¹ ∨ a ∈ rcns a✝}