LOGIC-KNOWLEDGE-TAKEN-FOR-GRANTED-INSTANCE.html -- ACL2 Version 6.3

### LOGIC-KNOWLEDGE-TAKEN-FOR-GRANTED-INSTANCE

a brief explanation of substitution instances

    Major Section:  INTRODUCTION-TO-THE-THEOREM-PROVER

Let p and q be terms or formulas (there is no difference in ACL2). Then we say p is an instance or substitution instance of q if and only if p can be obtained from q by uniformly replacing the variables of q by terms. Sometimes we call p the target and q the pattern because by choosing appropriate replacements we can make the pattern match many different targets.

For example, the following target is an instance of the given pattern:

    target:      (APP (APP (REV A) (REV B)) (REV C))
    pattern:     (APP (APP   x       y    ) (REV z))

The replacement or substitution used in this match of the pattern to the target is:

    variable in pattern          replacement term
    x                              (REV A)
    y                              (REV B)
    z                              C

Such substitutions are usually written this way in ACL2:

    ((x  (REV A))
     (y  (REV B))
     (z  C)).

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