Step
*
of Lemma
absval-diff-product-bound
∀u,v,x,y:ℕ. ((|u - v| * |x - y|) ≤ |(imax(u;v) * imax(x;y)) - imin(u;v) * imin(x;y)|)
BY
{ Assert ⌜∀u:ℕ. ∀v:ℕu. ∀x:ℕ. ∀y:ℕx. ((|u - v| * |x - y|) ≤ |(u * x) - v * y|)⌝⋅ }
1
.....assertion.....
∀u:ℕ. ∀v:ℕu. ∀x:ℕ. ∀y:ℕx. ((|u - v| * |x - y|) ≤ |(u * x) - v * y|)
2
1. ∀u:ℕ. ∀v:ℕu. ∀x:ℕ. ∀y:ℕx. ((|u - v| * |x - y|) ≤ |(u * x) - v * y|)
⊢ ∀u,v,x,y:ℕ. ((|u - v| * |x - y|) ≤ |(imax(u;v) * imax(x;y)) - imin(u;v) * imin(x;y)|)
Latex:
Latex:
\mforall{}u,v,x,y:\mBbbN{}. ((|u - v| * |x - y|) \mleq{} |(imax(u;v) * imax(x;y)) - imin(u;v) * imin(x;y)|)
By
Latex:
Assert \mkleeneopen{}\mforall{}u:\mBbbN{}. \mforall{}v:\mBbbN{}u. \mforall{}x:\mBbbN{}. \mforall{}y:\mBbbN{}x. ((|u - v| * |x - y|) \mleq{} |(u * x) - v * y|)\mkleeneclose{}\mcdot{}
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