Then, by applying the inductive hypothesis, for all i, there exists an integer [n.

Hence, we can apply the inductive hypothesis and get: [[Eta]'.

Hence, we can apply the inductive hypothesis and get that, for all i: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [r.

From the left premise ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), the right assumption ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), and the inductive hypothesis we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

From the premise ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), the constructed derivation ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), and the inductive hypothesis we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

From the premise ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), the right assumption ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), and the inductive hypothesis we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].