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Mirrors > Home > MPE Home > Th. List > df-dec | Structured version Visualization version GIF version |
Description: Define the "decimal constructor", which is used to build up "decimal integers" or "numeric terms" in base 10. For example, (;;;1000 + ;;;2000) = ;;;3000 1kp2ke3k 30204. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 1-Aug-2021.) |
Ref | Expression |
---|---|
df-dec | โข ;๐ด๐ต = (((9 + 1) ยท ๐ด) + ๐ต) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class ๐ด | |
2 | cB | . . 3 class ๐ต | |
3 | 1, 2 | cdc 12678 | . 2 class ;๐ด๐ต |
4 | c9 12275 | . . . . 5 class 9 | |
5 | c1 11110 | . . . . 5 class 1 | |
6 | caddc 11112 | . . . . 5 class + | |
7 | 4, 5, 6 | co 7404 | . . . 4 class (9 + 1) |
8 | cmul 11114 | . . . 4 class ยท | |
9 | 7, 1, 8 | co 7404 | . . 3 class ((9 + 1) ยท ๐ด) |
10 | 9, 2, 6 | co 7404 | . 2 class (((9 + 1) ยท ๐ด) + ๐ต) |
11 | 3, 10 | wceq 1533 | 1 wff ;๐ด๐ต = (((9 + 1) ยท ๐ด) + ๐ต) |
Colors of variables: wff setvar class |
This definition is referenced by: 9p1e10 12680 dfdec10 12681 decex 12682 deceq1 12683 deceq2 12684 deccl 12693 10re 12697 deccarry 46572 |
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