have ⟨z₂, a₁⟩ := Step.Apply.RTC.construct s₁ (s₁.output e₂.rcn)
α : Type
inst✝ : Proper α
s₁ s₂ s₃ : State α
e₁ : s₁ ↓ₛ s₂
e₂ : s₂ ↓ₑ s₃
h : rcn (skip e₁) ≮[s₁.rtr]≯ rcn (exec e₂)
⊢ ∃ s₂' s₃' e₁' e₂', rcn e₁' = rcn (exec e₂) ∧ rcn e₂' = rcn (skip e₁) ∧ s₃' = s₃
α : Type
inst✝ : Proper α
s₁ s₂ s₃ : State α
e₁ : s₁ ↓ₛ s₂
e₂ : s₂ ↓ₑ s₃
h : rcn (skip e₁) ≮[s₁.rtr]≯ rcn (exec e₂)
z₂ : State α
a₁ : s₁ -[output s₁ (Step.Exec.rcn e₂)]→ z₂
⊢ ∃ s₂' s₃' e₁' e₂', rcn e₁' = rcn (exec e₂) ∧ rcn e₂' = rcn (skip e₁) ∧ s₃' = s₃