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 ) } |
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 ) } |