Metamath Proof Explorer


Theorem knoppndvlem5

Description: Lemma for knoppndv . (Contributed by Asger C. Ipsen, 15-Jun-2021) (Revised by Asger C. Ipsen, 5-Jul-2021)

Ref Expression
Hypotheses knoppndvlem5.t T = x x + 1 2 x
knoppndvlem5.f F = y n 0 C n T 2 N n y
knoppndvlem5.a φ A
knoppndvlem5.c φ C
knoppndvlem5.n φ N
Assertion knoppndvlem5 φ i = 0 J F A i

Proof

Step Hyp Ref Expression
1 knoppndvlem5.t T = x x + 1 2 x
2 knoppndvlem5.f F = y n 0 C n T 2 N n y
3 knoppndvlem5.a φ A
4 knoppndvlem5.c φ C
5 knoppndvlem5.n φ N
6 fzfid φ 0 J Fin
7 5 adantr φ i 0 J N
8 4 adantr φ i 0 J C
9 3 adantr φ i 0 J A
10 elfznn0 i 0 J i 0
11 10 adantl φ i 0 J i 0
12 1 2 7 8 9 11 knoppcnlem3 φ i 0 J F A i
13 6 12 fsumrecl φ i = 0 J F A i