Metamath Proof Explorer
Description: Comparing two decimal integers (unequal higher places). (Contributed by AV, 8-Sep-2021)
|
|
Ref |
Expression |
|
Hypotheses |
declt.a |
⊢ 𝐴 ∈ ℕ0 |
|
|
declt.b |
⊢ 𝐵 ∈ ℕ0 |
|
|
declth.c |
⊢ 𝐶 ∈ ℕ0 |
|
|
declth.d |
⊢ 𝐷 ∈ ℕ0 |
|
|
declth.e |
⊢ 𝐶 ≤ 9 |
|
|
declth.l |
⊢ 𝐴 < 𝐵 |
|
Assertion |
declth |
⊢ ; 𝐴 𝐶 < ; 𝐵 𝐷 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
declt.a |
⊢ 𝐴 ∈ ℕ0 |
2 |
|
declt.b |
⊢ 𝐵 ∈ ℕ0 |
3 |
|
declth.c |
⊢ 𝐶 ∈ ℕ0 |
4 |
|
declth.d |
⊢ 𝐷 ∈ ℕ0 |
5 |
|
declth.e |
⊢ 𝐶 ≤ 9 |
6 |
|
declth.l |
⊢ 𝐴 < 𝐵 |
7 |
3 5
|
le9lt10 |
⊢ 𝐶 < ; 1 0 |
8 |
1 2 3 4 7 6
|
decltc |
⊢ ; 𝐴 𝐶 < ; 𝐵 𝐷 |