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Can someone explain this "constructive induction" needed to solve recursive equations?

For example, use "constructive induction" to show that the following is [tex]\Theta (n)[/tex]

[tex]T(n) = 1 \leftrightarrow n = 1,2[/tex]

[tex]T(n) = T\lceil n/4\rceil + T \lceil 2n/3\rceil + \Theta (n) \leftrightarrow n > 2[/tex]

For example, use "constructive induction" to show that the following is [tex]\Theta (n)[/tex]

[tex]T(n) = 1 \leftrightarrow n = 1,2[/tex]

[tex]T(n) = T\lceil n/4\rceil + T \lceil 2n/3\rceil + \Theta (n) \leftrightarrow n > 2[/tex]

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