Metamath Proof Explorer


Theorem declth

Description: Comparing two decimal integers (unequal higher places). (Contributed by AV, 8-Sep-2021)

Ref Expression
Hypotheses declt.a ⊢ A ∈ ℕ 0
declt.b ⊢ B ∈ ℕ 0
declth.c ⊢ C ∈ ℕ 0
declth.d ⊢ D ∈ ℕ 0
declth.e ⊢ C ≤ 9
declth.l ⊢ A < B
Assertion declth Could not format assertion : No typesetting found for |- ; A C < ; B D with typecode |-

Proof

Step Hyp Ref Expression
1 declt.a ⊢ A ∈ ℕ 0
2 declt.b ⊢ B ∈ ℕ 0
3 declth.c ⊢ C ∈ ℕ 0
4 declth.d ⊢ D ∈ ℕ 0
5 declth.e ⊢ C ≤ 9
6 declth.l ⊢ A < B
7 3 5 le9lt10 ⊢ C < 10
8 1 2 3 4 7 6 decltc Could not format ; A C < ; B D : No typesetting found for |- ; A C < ; B D with typecode |-