Step |
Hyp |
Ref |
Expression |
1 |
|
simp1 |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> F e. V ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> F e. V ) with typecode |- |
2 |
|
itcoval |
Could not format ( F e. V -> ( IterComp ` F ) = seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ) : No typesetting found for |- ( F e. V -> ( IterComp ` F ) = seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ) with typecode |- |
3 |
2
|
fveq1d |
Could not format ( F e. V -> ( ( IterComp ` F ) ` ( Y + 1 ) ) = ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` ( Y + 1 ) ) ) : No typesetting found for |- ( F e. V -> ( ( IterComp ` F ) ` ( Y + 1 ) ) = ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` ( Y + 1 ) ) ) with typecode |- |
4 |
1 3
|
syl |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( ( IterComp ` F ) ` ( Y + 1 ) ) = ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` ( Y + 1 ) ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( ( IterComp ` F ) ` ( Y + 1 ) ) = ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` ( Y + 1 ) ) ) with typecode |- |
5 |
|
nn0uz |
|
6 |
|
simp2 |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> Y e. NN0 ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> Y e. NN0 ) with typecode |- |
7 |
|
eqid |
|
8 |
2
|
adantr |
Could not format ( ( F e. V /\ Y e. NN0 ) -> ( IterComp ` F ) = seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 ) -> ( IterComp ` F ) = seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ) with typecode |- |
9 |
8
|
fveq1d |
Could not format ( ( F e. V /\ Y e. NN0 ) -> ( ( IterComp ` F ) ` Y ) = ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` Y ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 ) -> ( ( IterComp ` F ) ` Y ) = ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` Y ) ) with typecode |- |
10 |
9
|
eqeq1d |
Could not format ( ( F e. V /\ Y e. NN0 ) -> ( ( ( IterComp ` F ) ` Y ) = G <-> ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` Y ) = G ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 ) -> ( ( ( IterComp ` F ) ` Y ) = G <-> ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` Y ) = G ) ) with typecode |- |
11 |
10
|
biimp3a |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` Y ) = G ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` Y ) = G ) with typecode |- |
12 |
|
eqidd |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) = ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) = ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) with typecode |- |
13 |
|
nn0p1gt0 |
|
14 |
13
|
3ad2ant2 |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> 0 < ( Y + 1 ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> 0 < ( Y + 1 ) ) with typecode |- |
15 |
14
|
gt0ne0d |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( Y + 1 ) =/= 0 ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( Y + 1 ) =/= 0 ) with typecode |- |
16 |
15
|
adantr |
Could not format ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> ( Y + 1 ) =/= 0 ) : No typesetting found for |- ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> ( Y + 1 ) =/= 0 ) with typecode |- |
17 |
|
neeq1 |
|
18 |
17
|
adantl |
Could not format ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> ( i =/= 0 <-> ( Y + 1 ) =/= 0 ) ) : No typesetting found for |- ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> ( i =/= 0 <-> ( Y + 1 ) =/= 0 ) ) with typecode |- |
19 |
16 18
|
mpbird |
Could not format ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> i =/= 0 ) : No typesetting found for |- ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> i =/= 0 ) with typecode |- |
20 |
19
|
neneqd |
Could not format ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> -. i = 0 ) : No typesetting found for |- ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> -. i = 0 ) with typecode |- |
21 |
20
|
iffalsed |
Could not format ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> if ( i = 0 , ( _I |` dom F ) , F ) = F ) : No typesetting found for |- ( ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) /\ i = ( Y + 1 ) ) -> if ( i = 0 , ( _I |` dom F ) , F ) = F ) with typecode |- |
22 |
|
peano2nn0 |
|
23 |
22
|
3ad2ant2 |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( Y + 1 ) e. NN0 ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( Y + 1 ) e. NN0 ) with typecode |- |
24 |
12 21 23 1
|
fvmptd |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ` ( Y + 1 ) ) = F ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ` ( Y + 1 ) ) = F ) with typecode |- |
25 |
5 6 7 11 24
|
seqp1d |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` ( Y + 1 ) ) = ( G ( g e. _V , j e. _V |-> ( F o. g ) ) F ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( seq 0 ( ( g e. _V , j e. _V |-> ( F o. g ) ) , ( i e. NN0 |-> if ( i = 0 , ( _I |` dom F ) , F ) ) ) ` ( Y + 1 ) ) = ( G ( g e. _V , j e. _V |-> ( F o. g ) ) F ) ) with typecode |- |
26 |
4 25
|
eqtrd |
Could not format ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( ( IterComp ` F ) ` ( Y + 1 ) ) = ( G ( g e. _V , j e. _V |-> ( F o. g ) ) F ) ) : No typesetting found for |- ( ( F e. V /\ Y e. NN0 /\ ( ( IterComp ` F ) ` Y ) = G ) -> ( ( IterComp ` F ) ` ( Y + 1 ) ) = ( G ( g e. _V , j e. _V |-> ( F o. g ) ) F ) ) with typecode |- |