Definition df-toply1 19554

Description: Define a function which maps a coefficient function for a univariate polynomial to the corresponding polynomial object. (Contributed by Mario Carneiro, 12-Jun-2015.)

Assertion

Ref	Expression
df-toply1	|- toPoly1 = ( f e. _V |-> ( n e. ( NN0 ^m 1o ) |-> ( f ` ( n ` (/) ) ) ) )

Distinct variable group:   f, n

Detailed syntax breakdown of Definition df-toply1

Step	Hyp	Ref	Expression
1		ctp1 19549	. 2 class toPoly1
2		vf	. . 3 setvar f
3		cvv 3200	. . 3 class _V
4		vn	. . . 4 setvar n
5		cn0 11292	. . . . 5 class NN0
6		c1o 7553	. . . . 5 class 1o
7		cmap 7857	. . . . 5 class ^m
8	5, 6, 7	co 6650	. . . 4 class ( NN0 ^m 1o )
9		c0 3915	. . . . . 6 class (/)
10	4	cv 1482	. . . . . 6 class n
11	9, 10	cfv 5888	. . . . 5 class ( n ` (/) )
12	2	cv 1482	. . . . 5 class f
13	11, 12	cfv 5888	. . . 4 class ( f ` ( n ` (/) ) )
14	4, 8, 13	cmpt 4729	. . 3 class ( n e. ( NN0 ^m 1o ) |-> ( f ` ( n ` (/) ) ) )
15	2, 3, 14	cmpt 4729	. 2 class ( f e. _V |-> ( n e. ( NN0 ^m 1o ) |-> ( f ` ( n ` (/) ) ) ) )
16	1, 15	wceq 1483	1 wff toPoly1 = ( f e. _V |-> ( n e. ( NN0 ^m 1o ) |-> ( f ` ( n ` (/) ) ) ) )

This definition is referenced by: (None)