BFS-returns-fail-implies-not-reachable∀ n. ¬ reach(source, dest, n) ⊦ [BFS(source, dest; norfail)] norfail = failADD-preserves-INVdecl-03
835BFS-returns-fail-implies-not-reachable-proofBFS-returns-fail-implies-not-reachable-proof-info
The proof is valid.
if dest is not reachable, and BFS terminates, then it returns fail.../../../../specs/INV/export/unit.xmlINV../../../../specs/INV/export/INV-def/longlemmainfo.xmlINV-def../../../../specs/graph/export/unit.xmlgraph../../../../specs/graph/export/reachset-def/longlemmainfo.xmlreachset-def../../../../specs/nat_or_fail/export/unit.xmlnat_or_fail../../../../specs/nat_or_fail/export/disj/longlemmainfo.xmldisj../../../../../../lib/basic/specs/nat-basic2/export/unit.xmlnat-basic2../../../../../../lib/basic/specs/nat-basic2/export/c/longlemmainfo.xmlc../../../../../../lib/basic/specs/nat-basic2/export/unit.xmlnat-basic2../../../../../../lib/basic/specs/nat-basic2/export/a/longlemmainfo.xmla../../../../specs/INV/export/unit.xmlINV../../../../specs/INV/export/INV-nextlevel/longlemmainfo.xmlINV-nextlevel../../../../../../lib/basic/specs/set-union/export/unit.xmlset-union../../../../../../lib/basic/specs/set-union/export/del-e-01/longlemmainfo.xmldel-e-01../../../../../../lib/basic/specs/set-union/export/unit.xmlset-union../../../../../../lib/basic/specs/set-union/export/del-addeq-05/longlemmainfo.xmldel-addeq-05../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basic../../../../../../lib/basic/specs/set-basic/export/in-04/longlemmainfo.xmlin-04../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basic../../../../../../lib/basic/specs/set-basic/export/ne/longlemmainfo.xmlne../../../../../../lib/basic/specs/set-union/export/unit.xmlset-union../../../../../../lib/basic/specs/set-union/export/del-e-02/longlemmainfo.xmldel-e-02../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basic../../../../../../lib/basic/specs/set-basic/export/size-zero-01/longlemmainfo.xmlsize-zero-01../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basic../../../../../../lib/basic/specs/set-basic/export/ne-01/longlemmainfo.xmlne-01../../../../specs/INV/export/unit.xmlINV../../../../specs/INV/export/INV-init/longlemmainfo.xmlINV-init../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basic../../../../../../lib/basic/specs/set-basic/export/size-one-01/longlemmainfo.xmlsize-one-01../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basic../../../../../../lib/basic/specs/set-basic/export/one-size/longlemmainfo.xmlone-size../../../../../../lib/basic/specs/set-union/export/unit.xmlset-union../../../../../../lib/basic/specs/set-union/export/One/longlemmainfo.xmlOne