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Step * 1 1 1 1 of Lemma r-triangle-inequality

.....subterm..... T:t
1:n
1. x : ℝ
2. y : ℝ
3. bdd-diff(-(|x + y|);-(|λn.((x n) + (y n))|))
⊢ |x| + |y| ∈ ℕ+ ⟶ ℤ
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Latex:

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Latex:
.....subterm.....  T:t
1:n
1.  x  :  \mBbbR{}
2.  y  :  \mBbbR{}
3.  bdd-diff(-(|x  +  y|);-(|\mlambda{}n.((x  n)  +  (y  n))|))
\mvdash{}  |x|  +  |y|  \mmember{}  \mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}


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