Falseworks are temporary structures used in the building of bridges and other arched structures in order to hold the item in place until its building is sufficiently far advanced to support itself.
Formwork is made of panels and accessories that act as a mold to form a desired shape with concrete (for any pupose), Falsework is the temporary support structure for the form.
Hardie G.M. (1995) Building Construction Principals, Practices, and Materials. New Jersey: Prentice Hall. (Pg 116, paragraph 1)
A bracing unit to secure a formwork panel to falsework or to a previously poured concrete structure includes a pressurized fluid inflatable and expandable hose and a rigid abutment member for supporting the hose and holding it against the outside surface of the formwork panel.
In the erection of concrete structures, particularly concrete walls, the formwork panels or sections must be pressed against a falsework structure for the formwork or, when the concrete structure is being constructed in stages or lifts, against the previously poured sections of the structure.
As a result, it is not necessary for the individual formwork panels to slide along the falsework or on the previously poured concrete section, since an appropriate pressure is exercised over the entire length of the erected formwork with the pressure acting perpendicularly to the formwork.
After the concrete hardens, the falsework rings are released, but are lifted on the support frame so high that their lower portion still remains in the region of the outer edge of the cast wall ring.
Then, an outer falsework is attached and connected with the inner falsework for forming a circumferentially closed section of the wall, with concrete being poured into the space between the outer and inner falseworks.
With respect to the inner falseworks, "the same cross-section" means that the cross-sectional surfaces of the falsework boarding, i.e., the surfaces, which are surrounded by the circumferentially closed profiles of the boarding, in cross-section, have the same shape and size.