A twin-shaft turbine engine, comprising: - a high-pressure rotor comprising an impeller of a high-pressure compressor of the turbine engine and a vaned disk of a high-pressure turbine of the turbine engine, - a combustion chamber mounted axially between the high-pressure compressor and the high-pressure turbine, - two coaxial walls (60, 62) delimiting an annular air injection channel between them, which is connected to an annular bypass space of the combustion chamber, and which is intended to accelerate a cooling air flow for cooling the vanes of the vaned disk of the high-pressure turbine coming from said bypass space of the combustion chamber, - a first labyrinth seal comprising a static part (100, 101) securely connected to a first of said walls delimiting the injection channel, and a rotary part supported by a disk of the high-pressure rotor and comprising at least two annular ribs protruding toward said static part (100, 101), - a second labyrinth seal comprising a static part securely connected to a second of said walls delimiting the injection channel, and a rotary part securely connected to the rotary part of the first labyrinth seal, - an annular flange mounted opposite the upstream flank of the vaned disk of the high-pressure turbine and delimiting, with said upstream flank, a first upstream part of a cooling circuit of the vanes of said vaned disk, - a first annular cavity delimited by the downstream flank of the impeller, an inner case of the combustion chamber, said first wall delimiting the injection channel, the first labyrinth seal, and an annular wall extending axially so as to connect the impeller to said disk of the high-pressure rotor supporting the rotary part of the first labyrinth seal, - a second annular cavity into which the injection channel opens and which is delimited by the first labyrinth seal, the second labyrinth seal, and an annular wall connecting the respective rotary parts (84, 86) of these labyrinth seals and in which openings are formed for putting said second cavity in communication with said cooling circuit of the vanes of the vaned disk of the high-pressure turbine, - a third annular cavity that communicates with a channel for the flow of a primary gas stream of the turbine engine, and which is delimited at least by the second labyrinth seal and the annular flange, said turbine engine being characterized in that it comprises a plurality of channels formed in said static part (100, 101) of the first labyrinth seal and emerging into an annular cavity delimited by two (88a, 88b) of the ribs of the rotary part of the first labyrinth seal, so as to inject air coming from the injection channel therein. - a high-pressure rotor comprising an impeller of a high-pressure compressor of the turbine engine and a vaned disk of a high-pressure turbine of the turbine engine, - a combustion chamber mounted axially between the high-pressure compressor and the high-pressure turbine, - two coaxial walls (60, 62) delimiting an annular air injection channel between them, which is connected to an annular bypass space of the combustion chamber, and which is intended to accelerate a cooling air flow for cooling the vanes of the vaned disk of the high-pressure turbine coming from said bypass space of the combustion chamber, - a first labyrinth seal comprising a static part (100, 101) securely connected to a first of said walls delimiting the injection channel, and a rotary part supported by a disk of the high-pressure rotor and comprising at least two annular ribs protruding toward said static part (100, 101), - a second labyrinth seal comprising a static part securely connected to a second of said walls delimiting the injection channel, and a rotary part securely connected to the rotary part of the first labyrinth seal, - an annular flange mounted opposite the upstream flank of the vaned disk of the high-pressure turbine and delimiting, with said upstream flank, a first upstream part of a cooling circuit of the vanes of said vaned disk, - a first annular cavity delimited by the downstream flank of the impeller, an inner case of the combustion chamber, said first wall delimiting the injection channel, the first labyrinth seal, and an annular wall extending axially so as to connect the impeller to said disk of the high-pressure rotor supporting the rotary part of the first labyrinth seal, - a second annular cavity into which the injection channel opens and which is delimited by the first labyrinth seal, the second labyrinth seal, and an annular wall connecting the respective rotary parts (84, 86) of these labyrinth seals and in which openings are formed for putting said second cavity in communication with said cooling circuit of the vanes of the vaned disk of the high-pressure turbine, - a third annular cavity that communicates with a channel for the flow of a primary gas stream of the turbine engine, and which is delimited at least by the second labyrinth seal and the annular flange,