set v = the Vertex of G;
set IT = the inducedSubgraph of G,(G .reachableFrom the Vertex of G);
take the inducedSubgraph of G,(G .reachableFrom the Vertex of G) ; :: thesis: the inducedSubgraph of G,(G .reachableFrom the Vertex of G) is Component-like
thus the inducedSubgraph of G,(G .reachableFrom the Vertex of G) is Component-like ; :: thesis: verum