Step |
Hyp |
Ref |
Expression |
1 |
|
decma.a |
|- A e. NN0 |
2 |
|
decma.b |
|- B e. NN0 |
3 |
|
decma.c |
|- C e. NN0 |
4 |
|
decma.d |
|- D e. NN0 |
5 |
|
decma.m |
|- M = ; A B |
6 |
|
decma.n |
|- N = ; C D |
7 |
|
decaddc.e |
|- ( ( A + C ) + 1 ) = E |
8 |
|
decaddc.f |
|- F e. NN0 |
9 |
|
decaddc.2 |
|- ( B + D ) = ; 1 F |
10 |
|
10nn0 |
|- ; 1 0 e. NN0 |
11 |
|
dfdec10 |
|- ; A B = ( ( ; 1 0 x. A ) + B ) |
12 |
5 11
|
eqtri |
|- M = ( ( ; 1 0 x. A ) + B ) |
13 |
|
dfdec10 |
|- ; C D = ( ( ; 1 0 x. C ) + D ) |
14 |
6 13
|
eqtri |
|- N = ( ( ; 1 0 x. C ) + D ) |
15 |
|
dfdec10 |
|- ; 1 F = ( ( ; 1 0 x. 1 ) + F ) |
16 |
9 15
|
eqtri |
|- ( B + D ) = ( ( ; 1 0 x. 1 ) + F ) |
17 |
10 1 2 3 4 12 14 8 7 16
|
numaddc |
|- ( M + N ) = ( ( ; 1 0 x. E ) + F ) |
18 |
|
dfdec10 |
|- ; E F = ( ( ; 1 0 x. E ) + F ) |
19 |
17 18
|
eqtr4i |
|- ( M + N ) = ; E F |