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Step * 1 of Lemma mdist-difference


1. X : Type
2. d : metric(X)
3. x : X
4. a : X
5. b : X
⊢ (mdist(d;x;b) - mdist(d;a;b)) ≤ mdist(d;x;a)
BY
{ (InstLemma `mdist-triangle-inequality` [⌜X⌝;⌜d⌝;⌜x⌝;⌜a⌝;⌜b⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  X  :  Type
2.  d  :  metric(X)
3.  x  :  X
4.  a  :  X
5.  b  :  X
\mvdash{}  (mdist(d;x;b)  -  mdist(d;a;b))  \mleq{}  mdist(d;x;a)


By

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Latex:
(InstLemma  `mdist-triangle-inequality`  [\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}  THEN  Auto)

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