This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Split a decimal number into two parts. Base case: N = 0 .
(Contributed by Mario Carneiro, 16-Jul-2015) (Revised by AV, 8-Sep-2021)
|
|
Ref |
Expression |
|
Hypothesis |
decsplit0.1 |
⊢ 𝐴 ∈ ℕ0 |
|
Assertion |
decsplit0 |
⊢ ( ( 𝐴 · ( ; 1 0 ↑ 0 ) ) + 0 ) = 𝐴 |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
decsplit0.1 |
⊢ 𝐴 ∈ ℕ0 |
| 2 |
1
|
decsplit0b |
⊢ ( ( 𝐴 · ( ; 1 0 ↑ 0 ) ) + 0 ) = ( 𝐴 + 0 ) |
| 3 |
1
|
nn0cni |
⊢ 𝐴 ∈ ℂ |
| 4 |
3
|
addridi |
⊢ ( 𝐴 + 0 ) = 𝐴 |
| 5 |
2 4
|
eqtri |
⊢ ( ( 𝐴 · ( ; 1 0 ↑ 0 ) ) + 0 ) = 𝐴 |