Step |
Hyp |
Ref |
Expression |
1 |
|
itcovalpc.f |
|
2 |
|
nn0ex |
|
3 |
2
|
mptex |
|
4 |
1 3
|
eqeltri |
|
5 |
|
simpl |
|
6 |
|
simpr |
Could not format ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) : No typesetting found for |- ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) with typecode |- |
7 |
|
itcovalsucov |
Could not format ( ( F e. _V /\ y e. NN0 /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( F o. ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) ) : No typesetting found for |- ( ( F e. _V /\ y e. NN0 /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( F o. ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) ) with typecode |- |
8 |
4 5 6 7
|
mp3an2ani |
Could not format ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( F o. ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) ) : No typesetting found for |- ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( F o. ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) ) with typecode |- |
9 |
|
simpr |
|
10 |
|
simplr |
|
11 |
5
|
adantr |
|
12 |
10 11
|
nn0mulcld |
|
13 |
9 12
|
nn0addcld |
|
14 |
|
eqidd |
|
15 |
|
oveq1 |
|
16 |
15
|
cbvmptv |
|
17 |
1 16
|
eqtri |
|
18 |
17
|
a1i |
|
19 |
|
oveq1 |
|
20 |
13 14 18 19
|
fmptco |
|
21 |
9
|
nn0cnd |
|
22 |
12
|
nn0cnd |
|
23 |
10
|
nn0cnd |
|
24 |
21 22 23
|
addassd |
|
25 |
|
nn0cn |
|
26 |
25
|
mulid1d |
|
27 |
26
|
adantl |
|
28 |
27
|
eqcomd |
|
29 |
28
|
oveq2d |
|
30 |
|
simpr |
|
31 |
30
|
nn0cnd |
|
32 |
5
|
nn0cnd |
|
33 |
|
1cnd |
|
34 |
31 32 33
|
adddid |
|
35 |
29 34
|
eqtr4d |
|
36 |
35
|
oveq2d |
|
37 |
36
|
adantr |
|
38 |
24 37
|
eqtrd |
|
39 |
38
|
mpteq2dva |
|
40 |
20 39
|
eqtrd |
|
41 |
40
|
adantr |
Could not format ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( F o. ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) = ( n e. NN0 |-> ( n + ( C x. ( y + 1 ) ) ) ) ) : No typesetting found for |- ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( F o. ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) = ( n e. NN0 |-> ( n + ( C x. ( y + 1 ) ) ) ) ) with typecode |- |
42 |
8 41
|
eqtrd |
Could not format ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( n e. NN0 |-> ( n + ( C x. ( y + 1 ) ) ) ) ) : No typesetting found for |- ( ( ( y e. NN0 /\ C e. NN0 ) /\ ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( n e. NN0 |-> ( n + ( C x. ( y + 1 ) ) ) ) ) with typecode |- |
43 |
42
|
ex |
Could not format ( ( y e. NN0 /\ C e. NN0 ) -> ( ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( n e. NN0 |-> ( n + ( C x. ( y + 1 ) ) ) ) ) ) : No typesetting found for |- ( ( y e. NN0 /\ C e. NN0 ) -> ( ( ( IterComp ` F ) ` y ) = ( n e. NN0 |-> ( n + ( C x. y ) ) ) -> ( ( IterComp ` F ) ` ( y + 1 ) ) = ( n e. NN0 |-> ( n + ( C x. ( y + 1 ) ) ) ) ) ) with typecode |- |