Metamath Proof Explorer


Theorem dec0h

Description: Add a zero in the higher places. (Contributed by Mario Carneiro, 17-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Hypothesis dec0u.1
|- A e. NN0
Assertion dec0h
|- A = ; 0 A

Proof

Step Hyp Ref Expression
1 dec0u.1
 |-  A e. NN0
2 10nn0
 |-  ; 1 0 e. NN0
3 2 1 num0h
 |-  A = ( ( ; 1 0 x. 0 ) + A )
4 dfdec10
 |-  ; 0 A = ( ( ; 1 0 x. 0 ) + A )
5 3 4 eqtr4i
 |-  A = ; 0 A