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Metamath Proof Explorer

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 )