Definition df-lmat 29878

Description: Define a function converting words of words into matrices. (Contributed by Thierry Arnoux, 28-Aug-2020.)

Assertion

Ref	Expression
df-lmat	|- litMat = ( m e. _V |-> ( i e. ( 1 ... ( # ` m ) ) , j e. ( 1 ... ( # ` ( m ` 0 ) ) ) |-> ( ( m ` ( i - 1 ) ) ` ( j - 1 ) ) ) )

Distinct variable group:   i, j, m

Detailed syntax breakdown of Definition df-lmat

Step	Hyp	Ref	Expression
1		clmat 29877	. 2 class litMat
2		vm	. . 3 setvar m
3		cvv 3200	. . 3 class _V
4		vi	. . . 4 setvar i
5		vj	. . . 4 setvar j
6		c1 9937	. . . . 5 class 1
7	2	cv 1482	. . . . . 6 class m
8		chash 13117	. . . . . 6 class #
9	7, 8	cfv 5888	. . . . 5 class ( # ` m )
10		cfz 12326	. . . . 5 class ...
11	6, 9, 10	co 6650	. . . 4 class ( 1 ... ( # ` m ) )
12		cc0 9936	. . . . . . 7 class 0
13	12, 7	cfv 5888	. . . . . 6 class ( m ` 0 )
14	13, 8	cfv 5888	. . . . 5 class ( # ` ( m ` 0 ) )
15	6, 14, 10	co 6650	. . . 4 class ( 1 ... ( # ` ( m ` 0 ) ) )
16	5	cv 1482	. . . . . 6 class j
17		cmin 10266	. . . . . 6 class -
18	16, 6, 17	co 6650	. . . . 5 class ( j - 1 )
19	4	cv 1482	. . . . . . 7 class i
20	19, 6, 17	co 6650	. . . . . 6 class ( i - 1 )
21	20, 7	cfv 5888	. . . . 5 class ( m ` ( i - 1 ) )
22	18, 21	cfv 5888	. . . 4 class ( ( m ` ( i - 1 ) ) ` ( j - 1 ) )
23	4, 5, 11, 15, 22	cmpt2 6652	. . 3 class ( i e. ( 1 ... ( # ` m ) ) , j e. ( 1 ... ( # ` ( m ` 0 ) ) ) |-> ( ( m ` ( i - 1 ) ) ` ( j - 1 ) ) )
24	2, 3, 23	cmpt 4729	. 2 class ( m e. _V |-> ( i e. ( 1 ... ( # ` m ) ) , j e. ( 1 ... ( # ` ( m ` 0 ) ) ) |-> ( ( m ` ( i - 1 ) ) ` ( j - 1 ) ) ) )
25	1, 24	wceq 1483	1 wff litMat = ( m e. _V |-> ( i e. ( 1 ... ( # ` m ) ) , j e. ( 1 ... ( # ` ( m ` 0 ) ) ) |-> ( ( m ` ( i - 1 ) ) ` ( j - 1 ) ) ) )

This definition is referenced by:  lmatval  29879