Theorem 11multnc

Description: The product of 11 (as numeral) with a number (no carry). (Contributed by AV, 15-Jun-2021)

	Ref	Expression
Hypothesis	11multnc.n	$$⊢N\in {\mathbb{N}}_0$$
Assertion	11multnc	$$⊢\mathrm{<mi\; mathcolor="\#808">N</mi>}\cdot 11=\mathrm{<mi\; mathcolor="\#808">N</mi>\; <mi\; mathcolor="\#808">N</mi>}$$

Proof

Step	Hyp	Ref	Expression
1		11multnc.n	$$⊢N\in {\mathbb{N}}_0$$
2		1nn0	$$⊢1\in {\mathbb{N}}_0$$
3	1 2 2	decmulnc	Could not format ( N x. ; 1 1 ) = ; ( N x. 1 ) ( N x. 1 ) : No typesetting found for |- ( N x. ; 1 1 ) = ; ( N x. 1 ) ( N x. 1 ) with typecode |-
4	1	nn0cni	$$⊢N\in ℂ$$
5	4	mulid1i	$$⊢\mathrm{<mi\; mathcolor="\#808">N</mi>}\cdot 1=N$$
6	5 5	deceq12i	Could not format ; ( N x. 1 ) ( N x. 1 ) = ; N N : No typesetting found for |- ; ( N x. 1 ) ( N x. 1 ) = ; N N with typecode |-
7	3 6	eqtri	$$⊢\mathrm{<mi\; mathcolor="\#808">N</mi>}\cdot 11=\mathrm{<mi\; mathcolor="\#808">N</mi>\; <mi\; mathcolor="\#808">N</mi>}$$