Metamath Proof Explorer


Definition df-fsupp

Description: Define the property of a function to be finitely supported (in relation to a given zero). (Contributed by AV, 23-May-2019)

Ref Expression
Assertion df-fsupp finSupp = { ⟨ 𝑟 , 𝑧 ⟩ ∣ ( Fun 𝑟 ∧ ( 𝑟 supp 𝑧 ) ∈ Fin ) }

Detailed syntax breakdown

Step Hyp Ref Expression
0 cfsupp finSupp
1 vr 𝑟
2 vz 𝑧
3 1 cv 𝑟
4 3 wfun Fun 𝑟
5 csupp supp
6 2 cv 𝑧
7 3 6 5 co ( 𝑟 supp 𝑧 )
8 cfn Fin
9 7 8 wcel ( 𝑟 supp 𝑧 ) ∈ Fin
10 4 9 wa ( Fun 𝑟 ∧ ( 𝑟 supp 𝑧 ) ∈ Fin )
11 10 1 2 copab { ⟨ 𝑟 , 𝑧 ⟩ ∣ ( Fun 𝑟 ∧ ( 𝑟 supp 𝑧 ) ∈ Fin ) }
12 0 11 wceq finSupp = { ⟨ 𝑟 , 𝑧 ⟩ ∣ ( Fun 𝑟 ∧ ( 𝑟 supp 𝑧 ) ∈ Fin ) }