Catalysis of the reaction: 5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxylate + 2 H+ = 5-amino-1-(5-phospho-D-ribosyl)imidazole + CO2.
5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxylate carboxy-lyase