How do I use induction to show that the language of a grammar is contained in a given set? [duplicate]

Question

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• How to show that L = L(G)? 1 answer

Given that I have the grammar

$\qquad\displaystyle G_1 = (\{a, b, c, d\}, \{S, X, Y \}, S, \{S → XY, X → aXb, X → ab, Y → cYd, Y → cd\})$,

how am I supposed to prove that

$\qquad\displaystyle S(G1) ⊆ \{a^{n+1} b^{n+1} c^{m+1} d^{m+1} \mid n, m ≥ 0\}$

by using Induction?