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Definition df-mzp 37813
Description: Polynomials over 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 ∈ V ↦ (mzPolyCld‘𝑣))

Detailed syntax breakdown of Definition df-mzp
StepHypRef Expression
1 cmzp 37811 . 2 class mzPoly
2 vv . . 3 setvar 𝑣
3 cvv 3351 . . 3 class V
42cv 1630 . . . . 5 class 𝑣
5 cmzpcl 37810 . . . . 5 class mzPolyCld
64, 5cfv 6031 . . . 4 class (mzPolyCld‘𝑣)
76cint 4611 . . 3 class (mzPolyCld‘𝑣)
82, 3, 7cmpt 4863 . 2 class (𝑣 ∈ V ↦ (mzPolyCld‘𝑣))
91, 8wceq 1631 1 wff mzPoly = (𝑣 ∈ V ↦ (mzPolyCld‘𝑣))
Colors of variables: wff setvar class
This definition is referenced by:  mzpval  37821  dmmzp  37822
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