Theorem lpadlem1

Description: Lemma for the leftpad theorems. (Contributed by Thierry Arnoux, 7-Aug-2023)

	Ref	Expression
Hypothesis	lpadlem1.1	$$⊢\phi \to C\in S$$
Assertion	lpadlem1	$$⊢\phi \to \left(0..^L-\left|W\right|\right)\times \left\{C\right\}\in \mathrm{Word}S$$

Proof

Step	Hyp	Ref	Expression
1		lpadlem1.1	$$⊢\phi \to C\in S$$
2		fconst6g	$$⊢C\in S\to \left(\left(0..^L-\left|W\right|\right)\times \left\{C\right\}\right):\left(0..^L-\left|W\right|\right)⟶S$$
3		iswrdi	$$⊢\left(\left(0..^L-\left|W\right|\right)\times \left\{C\right\}\right):\left(0..^L-\left|W\right|\right)⟶S\to \left(0..^L-\left|W\right|\right)\times \left\{C\right\}\in \mathrm{Word}S$$
4	1 2 3	3syl	$$⊢\phi \to \left(0..^L-\left|W\right|\right)\times \left\{C\right\}\in \mathrm{Word}S$$