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Using awk:

$ awk -v RS= -v ORS='\n\n' '/^\[Profile/; /^\[Install/{for(i=1;i<=NF;i++) if ($i ~ /^Default=/) print $i}' 

Or

$ awk 'BEGIN{RS="";ORS="\n\n"} /^\[Profile/; /^\[Install/ && match($0,/\nDefault=[^[:space:]]+/){ print substr($0,RSTART,RLENGTH) }' file 

Using awk:

$ awk 'BEGIN{RS="";ORS="\n\n"} /^\[Profile/; /^\[Install/ && match($0,/\nDefault=[^[:space:]]+/){ print substr($0,RSTART,RLENGTH) }' file 

Using awk:

$ awk -v RS= -v ORS='\n\n' '/\[Profile/; /\[Install/{for(i=1;i<=NF;i++) if ($i ~ /^Default=/) print $i}' 

Or

$ awk 'BEGIN{RS="";ORS="\n\n"}   /\[Profile/;   /\[Install/ && match($0,/[[:space:]]Default=[^[:space:]]+/){   print substr($0,RSTART,RLENGTH)   }' file 

Using awk:

$ awk -v RS= -v ORS='\n\n' '/^\[Profile/; /^\[Install/{for(i=1;i<=NF;i++) if ($i ~ /^Default=/) print $i}' 

Or

$ awk 'BEGIN{RS="";ORS="\n\n"} /^\[Profile/; /^\[Install/ && match($0,/\nDefault=[^[:space:]]+/){ print substr($0,RSTART,RLENGTH) }' file 

Using awk:

$ awk -v RS= -v ORS='\n\n' ' /\[Profile/; /\[Install/{for(i=1;i<=NF;i++) if ($i ~ /^Default=/) print $i}' 

Using awk:

$ awk -v RS= -v ORS='\n\n' '/\[Profile/; /\[Install/{for(i=1;i<=NF;i++) if ($i ~ /^Default=/) print $i}' 

Or

$ awk 'BEGIN{RS="";ORS="\n\n"} /\[Profile/; /\[Install/ && match($0,/[[:space:]]Default=[^[:space:]]+/){ print substr($0,RSTART,RLENGTH) }' file