Metamath Proof Explorer


Theorem ackval41

Description: The Ackermann function at (4,1). (Contributed by AV, 9-May-2024)

Ref Expression
Assertion ackval41 Could not format assertion : No typesetting found for |- ( ( Ack ` 4 ) ` 1 ) = ; ; ; ; 6 5 5 3 3 with typecode |-

Proof

Step Hyp Ref Expression
1 ackval41a Could not format ( ( Ack ` 4 ) ` 1 ) = ( ( 2 ^ ; 1 6 ) - 3 ) : No typesetting found for |- ( ( Ack ` 4 ) ` 1 ) = ( ( 2 ^ ; 1 6 ) - 3 ) with typecode |-
2 6nn0 6 0
3 5nn0 5 0
4 2 3 deccl 65 0
5 4 3 deccl 655 0
6 3nn0 3 0
7 5 6 deccl 6553 0
8 2exp16 2 16 = 65536
9 3p1e4 3 + 1 = 4
10 eqid 6553 = 6553
11 5 6 9 10 decsuc 6553 + 1 = 6554
12 3cn 3
13 gbpart6 6 = 3 + 3
14 12 12 13 mvrraddi 6 3 = 3
15 7 2 6 8 11 14 decsubi 2 16 3 = 65533
16 1 15 eqtri Could not format ( ( Ack ` 4 ) ` 1 ) = ; ; ; ; 6 5 5 3 3 : No typesetting found for |- ( ( Ack ` 4 ) ` 1 ) = ; ; ; ; 6 5 5 3 3 with typecode |-