State machine exercises#20
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alexoltean61 merged 8 commits intoJun 1, 2026
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| lemma executeLemma {μ st} (h1 : Reachable (.ok μ) st) (h2 : isFinal st) : | ||
| ∃ fuel : ℕ, execute fuel μ = st := by | ||
| cases st with | ||
| | error => contradiction | ||
| | ok μx => | ||
| obtain ⟨m, hm⟩ := @executeLemmaAux 0 _ _ h1 | ||
| use m | ||
| rw [hm, execute] | ||
| simp [h2] |
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Nice! You actually came up with a simpler proof than mine. For reference, the statement of the lemma I came up with was:
lemma executeLemmaAux {μ st} (h : Reachable (.ok μ) st) :
(isFinal st → ∃ fuel : ℕ, execute fuel μ = st) ∧
(∀ μ', st = (.ok μ') → ¬isFinal (.ok μ') →
∀ fuel' : ℕ, ∃ fuel : ℕ, execute fuel μ = execute fuel' μ' ) := byWhich is correct, but painful to state & prove. Yours is much cleaner, well done.
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