Complex air supply system for gas turbine engine and associated aircraft

An aircraft air supply system comprising:

• a gas turbine engine including a fan and at least one compressor, the at least one compressor driven by at least one turbine section, and a combustor for combusting air from the at least one compressor and delivering it across at least one turbine;
• a lower pressure tap within the at least one compressor, and the lower pressure tap air being connected to a first heat exchanger to be cooled by cooling air, and then to a selection valve, the selection valve for selectively delivering the lower pressure tap air to a boost compressor, and lower pressure tap air downstream of the boost compressor being connected to cool the at least one turbine;
• and
• the selection valve for also selectively delivering a portion of the lower pressure tap air across a first cooling turbine, and to a line associated with an air delivery system for a cabin on an associated aircraft, and a portion of the air downstream of the first cooling turbine being connected to a second cooling turbine, and air downstream of the second cooling turbine being connected for use in a cold loop such that the lower pressure tap air downstream of the second cooling turbine is at a lower temperature than air downstream of the first cooling turbine.