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Step * of Lemma geo-cong-preserves-strict-bet-out

∀e:BasicGeometry. ∀a,b,c,a',b',c':Point.  (a-b-c ⇒ ab ≅ a'b' ⇒ ac ≅ a'c' ⇒ out(a' b'c') ⇒ a'-b'-c')
BY
{ TACTIC:(((Auto THEN D 0) THEN InstLemma `geo-cong-preserves-bet-out` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜a'⌝;⌜b'⌝;⌜c'⌝]⋅ THEN Auto)
          THEN InstLemma `geo-inner-three-segment` [⌜e⌝;⌜c⌝;⌜b⌝;⌜a⌝;⌜c'⌝;⌜b'⌝;⌜a'⌝]⋅
          THEN Auto) }

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Latex:

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Latex:
\mforall{}e:BasicGeometry.  \mforall{}a,b,c,a',b',c':Point.
    (a-b-c  {}\mRightarrow{}  ab  \mcong{}  a'b'  {}\mRightarrow{}  ac  \mcong{}  a'c'  {}\mRightarrow{}  out(a'  b'c')  {}\mRightarrow{}  a'-b'-c')


By

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Latex:
TACTIC:(((Auto  THEN  D  0)
                  THEN  InstLemma  `geo-cong-preserves-bet-out`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a'\mkleeneclose{};\mkleeneopen{}b'\mkleeneclose{};\mkleeneopen{}c'\mkleeneclose{}]\mcdot{}
                  THEN  Auto)
                THEN  InstLemma  `geo-inner-three-segment`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c'\mkleeneclose{};\mkleeneopen{}b'\mkleeneclose{};\mkleeneopen{}a'\mkleeneclose{}]\mcdot{}
                THEN  Auto)

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