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Require Import Arith List Bool. (* Q1: Define a function that adds up the first k odd numbers, 1, 3, 2 k - 1 (the value for 0 is 0). *) (* The following is a model of string searching in a text and decomposing a text into lines. *) (* Q2: Define a function headeq : list nat -> list nat -> bool, which returns true exactly when the first list is the head of the second one. *) (* Q3: Define a function index : list nat -> list nat -> bool, which returns true exactly when the first list occurs in the second one; use the previous function. *) (* Q4: Definition a function decompose : nat -> list nat -> list (list nat) which breaks down a list of numbers into the fragments separated by the number given as argument. Intuition: think of the natural number as the code for end of lines, we want to decompose a text into the list of lines. *) (* Q5: Define a function recompose : nat -> list (list nat) -> list nat so that (recompose fs) is the inverse of (decompose fs) *) (* Q6: Define a function replace : list nat -> list nat -> list nat -> list nat which substitutes every instance of the first argument with the second argument in the third argument. for instance replace (2::3::nil) (7::8::nil) (1::2::3::4::5::6::nil) should return 1::7::8::4::5::6 *)