Theorem lpadlem1

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

	Ref	Expression
Hypothesis	lpadlem1.1	|- ( ph -> C e. S )
Assertion	lpadlem1	|- ( ph -> ( ( 0 ..^ ( L - ( # ` W ) ) ) X. { C } ) e. Word S )

Proof

Step	Hyp	Ref	Expression
1		lpadlem1.1	|- ( ph -> C e. S )
2		fconst6g	|- ( C e. S -> ( ( 0 ..^ ( L - ( # ` W ) ) ) X. { C } ) : ( 0 ..^ ( L - ( # ` W ) ) ) --> S )
3		iswrdi	|- ( ( ( 0 ..^ ( L - ( # ` W ) ) ) X. { C } ) : ( 0 ..^ ( L - ( # ` W ) ) ) --> S -> ( ( 0 ..^ ( L - ( # ` W ) ) ) X. { C } ) e. Word S )
4	1 2 3	3syl	|- ( ph -> ( ( 0 ..^ ( L - ( # ` W ) ) ) X. { C } ) e. Word S )