grep1-5  Exercise 1: ids and a Name Chosen by Something Later in the Line
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cat > users.txt <<'EOF'
user=bob id=42 role=admin
user=alice id=7 role=user
user=carol id=19 role=user
EOF

echo "ids:"
grep -oP 'id=\K\d+' users.txt
echo
echo "names of users whose role is user:"
grep -oP 'user=\K\w+(?=.*role=user)' users.txt

Output:

ids:
42
7
19

names of users whose role is user:
alice
carol

WHY THIS WORKS AS AN ANSWER
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id=\K\d+ matches 'id=' and then \K throws it away, so only the digits are printed. In the second command the name is what we print; (?=.*role=user) is a lookahead that looks FORWARD along the line for role=user without including it in the output. Only alice and carol qualify.
A lookbehind cannot do the second job: the condition (role=user) comes AFTER the name on the line, and a lookbehind can only look at what is before the match. Even for conditions before the match, a lookbehind has to be a fixed length (Chapter 5), while \K has no such limit, which is why \K is the usual way to say 'start the output here'.