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Theorem BFS-returns-fail-implies-not-reachable

∀ n. ¬ reach(source, dest, n) ⊦ [BFS(source, dest; norfail)] norfail = fail

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: if dest is not reachable, and BFS terminates, then it returns fail.
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 35
Used lemmas: ADD-preserves-INV, decl-03,
Used spec theorems:
- INV/INV-def
- graph/reachset-def
Used simplifier rules: