Axially-shortening prosthetic valve

A method for use at an atrioventricular valve that has an annulus and is disposed between an atrium and a ventricle of a heart of a subject, the method comprising:

• transluminally advancing a catheter to the heart;
• via the catheter, advancing to the heart a prosthetic valve including:
• an upstream annular skirt,
• a downstream skirt having:
• a first portion defining a lumen therethrough, and
• a second portion circumscribing the first portion,
• a plurality of anchoring arms, each of the anchoring arms having a first end that is coupled to the second portion, and an opposite end that is a free end, and
• a plurality of prosthetic leaflets attached to the first portion and disposed within the lumen;
• expanding the upstream annular skirt in the atrium and expanding the anchoring arms in the ventricle such that:
• the upstream annular skirt becomes disposed over the annulus, and
• each of the anchoring arms becomes oriented to lead in a direction from the first end to the opposite end, the direction being radially outward and toward the upstream annular skirt;
• and
• subsequently to expanding the upstream annular skirt in the atrium, and while each of the anchoring arms remains oriented to lead in the direction from the first end to the opposite end, squeezing tissue of the atrioventricular valve between the upstream annular skirt and the anchoring arms by causing the second portion of the downstream skirt and the anchoring arms to move:
• (i) with respect to the prosthetic leaflets, and
• (ii) toward the upstream annular skirt.