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Step * 2 of Lemma ocmon_trans


1. ∀[g:OCMon]. ∀[a,b,c:|g|].  ((↑(a ≤b b)) ⇒ (↑(b ≤b c)) ⇒ (↑(a ≤b c)))
⊢ ∀[g:OCMon]. ∀[a,b,c:|g|].  (↑(a ≤b c)) supposing ((↑(b ≤b c)) and (↑(a ≤b b)))
BY
{ (Auto THEN InstHyp [⌜g⌝;⌜a⌝;⌜b⌝;⌜c⌝] 1⋅ THEN Auto) }

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Latex:

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Latex:

1.  \mforall{}[g:OCMon].  \mforall{}[a,b,c:|g|].    ((\muparrow{}(a  \mleq{}\msubb{}  b))  {}\mRightarrow{}  (\muparrow{}(b  \mleq{}\msubb{}  c))  {}\mRightarrow{}  (\muparrow{}(a  \mleq{}\msubb{}  c)))
\mvdash{}  \mforall{}[g:OCMon].  \mforall{}[a,b,c:|g|].    (\muparrow{}(a  \mleq{}\msubb{}  c))  supposing  ((\muparrow{}(b  \mleq{}\msubb{}  c))  and  (\muparrow{}(a  \mleq{}\msubb{}  b)))


By

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Latex:
(Auto  THEN  InstHyp  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]  1\mcdot{}  THEN  Auto)

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