Definition df-mzp 37287

Description: Polynomials over ZZ with an arbitrary index set, that is, the smallest ring of functions containing all constant functions and all projections. This is almost the most general reasonable definition; to reach full generality, we would need to be able to replace ZZ with an arbitrary (semi-)ring (and a coordinate subring), but rings have not been defined yet. (Contributed by Stefan O'Rear, 4-Oct-2014.)

Assertion

Ref	Expression
df-mzp	|- mzPoly = ( v e. _V |-> |^| (mzPolyCld ` v ) )

Detailed syntax breakdown of Definition df-mzp

Step	Hyp	Ref	Expression
1		cmzp 37285	. 2 class mzPoly
2		vv	. . 3 setvar v
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . . 5 class v
5		cmzpcl 37284	. . . . 5 class mzPolyCld
6	4, 5	cfv 5888	. . . 4 class (mzPolyCld ` v )
7	6	cint 4475	. . 3 class |^| (mzPolyCld ` v )
8	2, 3, 7	cmpt 4729	. 2 class ( v e. _V |-> |^| (mzPolyCld ` v ) )
9	1, 8	wceq 1483	1 wff mzPoly = ( v e. _V |-> |^| (mzPolyCld ` v ) )

This definition is referenced by:  mzpval  37295  dmmzp  37296