Datasets:
Tasks:
Text Generation
Modalities:
Text
Sub-tasks:
language-modeling
Languages:
English
Size:
100K - 1M
License:
File size: 600 Bytes
4365a98 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |
let EXAMPLE = prove
(`!n. nsum(0..n) (\i. i) = (n*(n + 1)) DIV 2`,
INDUCT_TAC THEN ASM_REWRITE_TAC[NSUM_CLAUSES_NUMSEG] THEN ARITH_TAC);;
let EXAMPLE_IN_MIZAR_LIGHT = thm `;
!n. nsum (0..n) (\i. i) = (n * (n + 1)) DIV 2 [1]
proof
nsum (0..0) (\i. i) = 0 [2] by NSUM_CLAUSES_NUMSEG;
... = (0 * (0 + 1)) DIV 2 [3] by ARITH_TAC;
!n. nsum (0..n) (\i. i) = (n * (n + 1)) DIV 2
==> nsum (0..SUC n) (\i. i) = (SUC n * (SUC n + 1)) DIV 2 [4]
proof
let n be num;
assume nsum (0..n) (\i. i) = (n * (n + 1)) DIV 2 [5];
qed by #;
qed by INDUCT_TAC from 3,4`;;
|