Definition df-frmd 15518

Description: Define a free monoid over a set i of generators, defined as the set of finite strings on I with the operation of concatenation. (Contributed by Mario Carneiro, 27-Sep-2015.)

Assertion

Ref	Expression
df-frmd	|- freeMnd = ( i e. _V |-> { <. ( Base ` ndx ) , Word i >. , <. ( +g ` ndx ) , ( concat |` (Word i X. Word i ) ) >. } )

Detailed syntax breakdown of Definition df-frmd

Step	Hyp	Ref	Expression
1		cfrmd 15516	. 2 class freeMnd
2		vi	. . 3 setvar i
3		cvv 2967	. . 3 class _V
4		cnx 14163	. . . . . 6 class ndx
5		cbs 14166	. . . . . 6 class Base
6	4, 5	cfv 5413	. . . . 5 class ( Base ` ndx )
7	2	cv 1368	. . . . . 6 class i
8	7	cword 12213	. . . . 5 class Word i
9	6, 8	cop 3878	. . . 4 class <. ( Base ` ndx ) , Word i >.
10		cplusg 14230	. . . . . 6 class +g
11	4, 10	cfv 5413	. . . . 5 class ( +g ` ndx )
12		cconcat 12215	. . . . . 6 class concat
13	8, 8	cxp 4833	. . . . . 6 class (Word i X. Word i )
14	12, 13	cres 4837	. . . . 5 class ( concat |` (Word i X. Word i ) )
15	11, 14	cop 3878	. . . 4 class <. ( +g ` ndx ) , ( concat |` (Word i X. Word i ) ) >.
16	9, 15	cpr 3874	. . 3 class { <. ( Base ` ndx ) , Word i >. , <. ( +g ` ndx ) , ( concat |` (Word i X. Word i ) ) >. }
17	2, 3, 16	cmpt 4345	. 2 class ( i e. _V |-> { <. ( Base ` ndx ) , Word i >. , <. ( +g ` ndx ) , ( concat |` (Word i X. Word i ) ) >. } )
18	1, 17	wceq 1369	1 wff freeMnd = ( i e. _V |-> { <. ( Base ` ndx ) , Word i >. , <. ( +g ` ndx ) , ( concat |` (Word i X. Word i ) ) >. } )

This definition is referenced by:  frmdval  15520