Definition df-dec

Description: Define the "decimal constructor", which is used to build up "decimal integers" or "numeric terms" in base 1 0 . For example, ( ; ; ; 1 0 0 0 + ; ; ; 2 0 0 0 ) = ; ; ; 3 0 0 0 1kp2ke3k . (Contributed by Mario Carneiro, 17-Apr-2015) (Revised by AV, 1-Aug-2021)

	Ref	Expression
Assertion	df-dec	|- ; A B = ( ( ( 9 + 1 ) x. A ) + B )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	|- A
1		cB	|- B
2	0 1	cdc	|- ; A B
3		c9	|- 9
4		caddc	|- +
5		c1	|- 1
6	3 5 4	co	|- ( 9 + 1 )
7		cmul	|- x.
8	6 0 7	co	|- ( ( 9 + 1 ) x. A )
9	8 1 4	co	|- ( ( ( 9 + 1 ) x. A ) + B )
10	2 9	wceq	|- ; A B = ( ( ( 9 + 1 ) x. A ) + B )