Description: Value of the decimal point construct. (Contributed by Thierry Arnoux, 16-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dpval2.a | ⊢ 𝐴 ∈ ℕ0 | |
dpval2.b | ⊢ 𝐵 ∈ ℝ | ||
Assertion | dpval2 | ⊢ ( 𝐴 . 𝐵 ) = ( 𝐴 + ( 𝐵 / ; 1 0 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dpval2.a | ⊢ 𝐴 ∈ ℕ0 | |
2 | dpval2.b | ⊢ 𝐵 ∈ ℝ | |
3 | dpval | ⊢ ( ( 𝐴 ∈ ℕ0 ∧ 𝐵 ∈ ℝ ) → ( 𝐴 . 𝐵 ) = _ 𝐴 𝐵 ) | |
4 | 1 2 3 | mp2an | ⊢ ( 𝐴 . 𝐵 ) = _ 𝐴 𝐵 |
5 | df-dp2 | ⊢ _ 𝐴 𝐵 = ( 𝐴 + ( 𝐵 / ; 1 0 ) ) | |
6 | 4 5 | eqtri | ⊢ ( 𝐴 . 𝐵 ) = ( 𝐴 + ( 𝐵 / ; 1 0 ) ) |