[ BeginEnv "proposition" , Label "formula_test_forall" , BeginEnv "math" , Command "forall" , Variable "x" , Symbol "," , Variable "y" , Symbol "." , Variable "x" , Symbol "=" , Variable "x" , Command "land" , Variable "y" , Symbol "=" , Variable "y" , EndEnv "math" , Symbol "." , EndEnv "proposition" , BeginEnv "proposition" , Label "formula_test_exists" , BeginEnv "math" , Command "exists" , Variable "x" , Symbol "," , Variable "y" , Symbol "." , Variable "x" , Symbol "=" , Variable "y" , EndEnv "math" , Symbol "." , EndEnv "proposition" , BeginEnv "proposition" , Label "formula_test_not_exists" , BeginEnv "math" , Command "exists" , Variable "x" , Symbol "," , Variable "y" , Symbol "." , Variable "x" , Symbol "=" , Variable "y" , EndEnv "math" , Word "if" , Word "and" , Word "only" , Word "if" , Word "not" , BeginEnv "math" , Command "exists" , Variable "x" , Symbol "." , Variable "x" , Command "neq" , Variable "x" , EndEnv "math" , Symbol "." , EndEnv "proposition" ]