A system for internally insulating buildings in particular slanted roofs, the system comprising: a particularly wooden base structure including rafters or beams, the rafters and beams being subsequently referred to as rafter elements, slats and/or profile strips, the slats and the profile strips being subsequently referred to as slat elements (10, 32), which slat elements (10, 32) are transversally arranged at the rafter elements and at a distance from the rafter elements and at a distance from each other, insulation elements arranged from an interior of a room at the rafter elements and between the rafter elements and the slat elements (10, 32) for thermal and/or sound insulation, in particular made from mineral wool forming an inner insulation placed in front of the rafter elements, which is subsequently referred to as an under rafter insulation, and attachment devices for supporting the insulation elements and for attaching the slat elements (10, 32) at the rafter elements offset therefrom for forming a support lattice structure at which a covering towards an interior of the room that is in particular made from sheet rock plates is attachable, wherein each attachment device is formed from a base element that is attachable at the rafter element and an attachment element that is adjustable relative to the base element and interlockable at the rafter element in a predetermined adjustment position, and wherein a receiving element (50, 78) for receiving the slat element (10, 32) is arranged at the end of the attachment element that is remote from the rafter element, characterized in that the attachment element is configured as an overreaching element placeable on the base element in an overreaching arrangement, and that the attachment element is configured as a section of an extruded profile which is configured from two parallel longitudinal arms (152, 154) which define a receiving cavity between each other for a penetration by the upper section of the base element, wherein in a portion of the two parallel longitudinal arms (152, 154) which define the receiving cavity between each other, an engagement profile is provided at the longitudinal arms (152, 154) and a complementary engagement profile is provided at the base element, such that by placing the attachment element onto the base element under respective pressure a relative elevational adjustment between the attachment element and the base element is performed such that the attachment element and the base element are anchored to each other due to the spring force of both longitudinal arms (152, 154) when both engagement profiles mesh. a particularly wooden base structure including rafters or beams, the rafters and beams being subsequently referred to as rafter elements, slats and/or profile strips, the slats and the profile strips being subsequently referred to as slat elements (10, 32), which slat elements (10, 32) are transversally arranged at the rafter elements and at a distance from the rafter elements and at a distance from each other, insulation elements arranged from an interior of a room at the rafter elements and between the rafter elements and the slat elements (10, 32) for thermal and/or sound insulation, in particular made from mineral wool forming an inner insulation placed in front of the rafter elements, which is subsequently referred to as an under rafter insulation, and attachment devices for supporting the insulation elements and for attaching the slat elements (10, 32) at the rafter elements offset therefrom for forming a support lattice structure at which a covering towards an interior of the room that is in particular made from sheet rock plates is attachable, wherein each attachment device is formed from a base element that is attachable at the rafter element and an attachment element that is adjustable relative to the base element and interlockable at the rafter element in a predetermined adjustment position, and wherein a receiving element (50, 78) for receiving the slat element (10, 32) is arranged at the end of the attachment element that is remote from the rafter element, characterized in that the attachment element is configured as an overreaching element placeable on the base element in an overreaching arrangement, and that the attachment element is configured as a section of an extruded profile which is configured from two parallel longitudinal arms (152, 154) which define a receiving cavity between each other for a penetration by the upper section of the base element, wherein in a portion of the two parallel longitudinal arms (152, 154) which define the receiving cavity between each other, an engagement profile is provided at the longitudinal arms (152, 154) and a complementary engagement profile is provided at the base element, such that by placing the attachment element onto the base element under respective pressure a relative elevational adjustment between the attachment element and the base element is performed such that the attachment element and the base element are anchored to each other due to the spring force of both longitudinal arms (152, 154) when both engagement profiles mesh.