Description: Split a decimal number into two parts. Base case: N = 1 . (Contributed by Mario Carneiro, 16-Jul-2015) (Revised by AV, 8-Sep-2021)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | decsplit0.1 | |- A e. NN0 |
|
| Assertion | decsplit1 | |- ( ( A x. ( ; 1 0 ^ 1 ) ) + B ) = ; A B |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | decsplit0.1 | |- A e. NN0 |
|
| 2 | 10nn0 | |- ; 1 0 e. NN0 |
|
| 3 | 2 | numexp1 | |- ( ; 1 0 ^ 1 ) = ; 1 0 |
| 4 | 3 | oveq2i | |- ( A x. ( ; 1 0 ^ 1 ) ) = ( A x. ; 1 0 ) |
| 5 | 2 | nn0cni | |- ; 1 0 e. CC |
| 6 | 1 | nn0cni | |- A e. CC |
| 7 | 5 6 | mulcomi | |- ( ; 1 0 x. A ) = ( A x. ; 1 0 ) |
| 8 | 4 7 | eqtr4i | |- ( A x. ( ; 1 0 ^ 1 ) ) = ( ; 1 0 x. A ) |
| 9 | 8 | oveq1i | |- ( ( A x. ( ; 1 0 ^ 1 ) ) + B ) = ( ( ; 1 0 x. A ) + B ) |
| 10 | dfdec10 | |- ; A B = ( ( ; 1 0 x. A ) + B ) |
|
| 11 | 9 10 | eqtr4i | |- ( ( A x. ( ; 1 0 ^ 1 ) ) + B ) = ; A B |