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Step * of Lemma geo-left_functionality

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∀e:EuclideanPlane. ∀a1,a2,b1,b2,c1,c2:Point.  (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1 leftof b1c1 ⇐⇒ a2 leftof b2c2))
BY
{ (((D 0 THENA Auto) THEN (InstLemma  `geo-sep-sym` [⌜e⌝] ⋅ THENA Auto))
   THEN (Assert ⌜∀a1,a2,b1,b2,c1,c2:Point.  (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ a1 leftof b1c1 ⇒ a2 leftof b2c2)⌝⋅
        THENM (Auto THEN InstHyp [⌜a2⌝;⌜a1⌝;⌜b2⌝;⌜b1⌝;⌜c2⌝;⌜c1⌝] 3⋅ THEN Auto)
        )
   ) }

1
.....assertion..... 
1. e : EuclideanPlane
2. ∀a,b:Point.  (a # b ⇒ b # a)
⊢ ∀a1,a2,b1,b2,c1,c2:Point.  (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ a1 leftof b1c1 ⇒ a2 leftof b2c2)

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Latex:

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Latex:
No  Annotations
\mforall{}e:EuclideanPlane.  \mforall{}a1,a2,b1,b2,c1,c2:Point.
    (a1  \mequiv{}  a2  {}\mRightarrow{}  b1  \mequiv{}  b2  {}\mRightarrow{}  c1  \mequiv{}  c2  {}\mRightarrow{}  (a1  leftof  b1c1  \mLeftarrow{}{}\mRightarrow{}  a2  leftof  b2c2))


By

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Latex:
(((D  0  THENA  Auto)  THEN  (InstLemma    `geo-sep-sym`  [\mkleeneopen{}e\mkleeneclose{}]  \mcdot{}  THENA  Auto))
  THEN  (Assert  \mkleeneopen{}\mforall{}a1,a2,b1,b2,c1,c2:Point.
                                  (a1  \mequiv{}  a2  {}\mRightarrow{}  b1  \mequiv{}  b2  {}\mRightarrow{}  c1  \mequiv{}  c2  {}\mRightarrow{}  a1  leftof  b1c1  {}\mRightarrow{}  a2  leftof  b2c2)\mkleeneclose{}\mcdot{}
            THENM  (Auto  THEN  InstHyp  [\mkleeneopen{}a2\mkleeneclose{};\mkleeneopen{}a1\mkleeneclose{};\mkleeneopen{}b2\mkleeneclose{};\mkleeneopen{}b1\mkleeneclose{};\mkleeneopen{}c2\mkleeneclose{};\mkleeneopen{}c1\mkleeneclose{}]  3\mcdot{}  THEN  Auto)
            )
  )

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