src/HOL/Isar_examples/Summation.thy
changeset 7869 c007f801cd59
parent 7800 8ee919e42174
child 7968 964b65b4e433
equal deleted inserted replaced
7868:0cb6508f190c 7869:c007f801cd59
    28   "SUM i < k. b" == "sum (%i. b) k";
    28   "SUM i < k. b" == "sum (%i. b) k";
    29 
    29 
    30 
    30 
    31 subsection {* Summation laws *};
    31 subsection {* Summation laws *};
    32 
    32 
    33 verbatim {* \begin{comment} *};
    33 text_raw {* \begin{comment} *};
    34 
    34 
    35 (* FIXME binary arithmetic does not yet work here *)
    35 (* FIXME binary arithmetic does not yet work here *)
    36 
    36 
    37 syntax
    37 syntax
    38   "3" :: nat  ("3")
    38   "3" :: nat  ("3")
    44   "4" == "Suc 3"
    44   "4" == "Suc 3"
    45   "6" == "Suc (Suc 4)";
    45   "6" == "Suc (Suc 4)";
    46 
    46 
    47 theorems [simp] = add_mult_distrib add_mult_distrib2 mult_ac;
    47 theorems [simp] = add_mult_distrib add_mult_distrib2 mult_ac;
    48 
    48 
    49 verbatim {* \end{comment} *};
    49 text_raw {* \end{comment} *};
    50 
    50 
    51 
    51 
    52 theorem sum_of_naturals:
    52 theorem sum_of_naturals:
    53   "2 * (SUM i < n + 1. i) = n * (n + 1)"
    53   "2 * (SUM i < n + 1. i) = n * (n + 1)"
    54   (is "?P n" is "?S n = _");
    54   (is "?P n" is "?S n = _");