[ [ BeginEnv "datatype" , Label "propform" , Word "define" , BeginEnv "math" , Command "propform" , EndEnv "math" , Word "inductively" , Word "as" , Word "follows" , Symbol "." , BeginEnv "enumerate" , Command "item" , BeginEnv "math" , Command "propbot" , Command "in" , Command "propform" , EndEnv "math" , Symbol "." , Command "item" , BeginEnv "math" , Command "propvar" , InvisibleBraceL , Variable "n" , InvisibleBraceR , Command "in" , Command "propform" , EndEnv "math" , Word "for" , BeginEnv "math" , Variable "n" , Command "in" , VisibleBraceL , Command "emptyset" , VisibleBraceR , EndEnv "math" , Symbol "." , Command "item" , BeginEnv "math" , ParenL , Variable "p" , Command "propto" , Variable "q" , ParenR , Command "in" , Command "propform" , EndEnv "math" , Word "for" , BeginEnv "math" , Variable "p" , Command "in" , Command "propform" , EndEnv "math" , Word "and" , BeginEnv "math" , Variable "q" , Command "in" , Command "propform" , EndEnv "math" , Symbol "." , EndEnv "enumerate" , EndEnv "datatype" ] , [ BeginEnv "proposition" , Label "propform_bot_test" , BeginEnv "math" , Command "propbot" , Command "in" , Command "propform" , EndEnv "math" , Symbol "." , EndEnv "proposition" ] , [ BeginEnv "proposition" , Label "propform_var_test" , Word "if" , BeginEnv "math" , Command "emptyset" , Command "in" , VisibleBraceL , Command "emptyset" , VisibleBraceR , EndEnv "math" , Symbol "," , Word "then" , BeginEnv "math" , Command "propvar" , InvisibleBraceL , Command "emptyset" , InvisibleBraceR , Command "in" , Command "propform" , EndEnv "math" , Symbol "." , EndEnv "proposition" ] , [ BeginEnv "proposition" , Label "propform_imp_test" , BeginEnv "math" , ParenL , Command "propbot" , Command "propto" , Command "propbot" , ParenR , Command "in" , Command "propform" , EndEnv "math" , Symbol "." , EndEnv "proposition" ] , [ BeginEnv "proposition" , Label "propform_distinct_test" , BeginEnv "math" , Command "propbot" , Command "neq" , ParenL , Command "propbot" , Command "propto" , Command "propbot" , ParenR , EndEnv "math" , Symbol "." , EndEnv "proposition" ] , [ BeginEnv "proposition" , Label "propform_injective_test" , Word "if" , BeginEnv "math" , Command "propvar" , InvisibleBraceL , Variable "x" , InvisibleBraceR , Symbol "=" , Command "propvar" , InvisibleBraceL , Variable "y" , InvisibleBraceR , EndEnv "math" , Symbol "," , Word "then" , BeginEnv "math" , Variable "x" , Symbol "=" , Variable "y" , EndEnv "math" , Symbol "." , EndEnv "proposition" ] ]