An extension of unification to substitutions with an application to automatic theorem proving

The notion of unifiability is extended to substitutions. Theorems concerning this notion are derived together with an algorithm for computing the most general unifier of a set of substitutions. Especially fruit full is the application in the case of the and-or tree approach to theorem proving where the subgoals are not independent but contain the same variables. Here the ultimate solution is shown to be the most general instance of the solutions to the individual subproblems. Another application concerns connection graphs where the arcs are substitutions and new arcs can be generated from old arcs.