equal
deleted
inserted
replaced
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 = _"); |