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Partial solution theorem
Let S be a system of formulas with the variables x1, . . . , xk and T be a system of formulas with the variables x1, . . . , xk, . . . , xn. The following are equivalent:
| (i) | Every real solution of S is a partial real solution of T. |
| (ii) | Every real solution of S is a partial hyperreal solution of T. |
| (iii) | Every hyperreal solution of S is a partial hyperreal solution of T. |