Research Article
The Gauge Integral Theory in HOL4
Table 2
The lemmas proving Theorem
19.
| Name of lemma | Description in HOL4 |
| DIVISION_LE_SUC | . division (a, b) d ==> n. d n <= d (SUC n) | DIVISION_MONO_LE | . division (a, b) d ==> m n. m <= n ==> d m <= d n | DIVISION_MONO_LE_SUC | . division (a, b) d ==> n. d n <= d (SUC n) | DIVISION_INTERMEDIATE | . division (a, b) d a <= c c <= b ==> n. n <= dsize d d n <= c c <= d (SUC n) | DIVISION_DSIZE_LE | . division (a, b) d (d (SUC n) = d n) ==> dsize d <= n | DIVISION_DSIZE_GE | . division (a, b) d d n < d (SUC n) ==> SUC n <= dsize d | DIVISION_DSIZE_EQ | ∀ . division (a, b) d d n < d (SUC n) (d (SUC (SUC n)) = d (SUC n)) ==> (dsize d = SUC n) | DIVISION_DSIZE_EQ_ALT | . division (a, b) d (d (SUC n) = d n) (∀ i. i < n ==> d i < d (SUC i)) ==> (dsize d = n) |
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