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 ∈ ℕ0
Assertion	dec0h	⊢ 𝐴 = ; 0 𝐴

Proof

Step	Hyp	Ref	Expression
1		dec0u.1	⊢ 𝐴 ∈ ℕ0
2		10nn0	⊢ ; 1 0 ∈ ℕ0
3	2 1	num0h	⊢ 𝐴 = ( ( ; 1 0 · 0 ) + 𝐴 )
4		dfdec10	⊢ ; 0 𝐴 = ( ( ; 1 0 · 0 ) + 𝐴 )
5	3 4	eqtr4i	⊢ 𝐴 = ; 0 𝐴