Step * of Lemma cong3-in-half-plane

e:EuclideanPlane. ∀a,b,c,x,y,u:Point.
  (c ab  xy  ab ≅ xy  (∃z:Point. (Cong3(abc,xyz) ∧ xy ∧ (u leftof xy ⇐⇒ leftof xy))))
BY
(Auto
   THEN (InstLemma `Euclid-drop-perp-1` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅
         THENA (Auto THEN InstLemma  `lsep-iff-all-sep` [⌜e⌝;⌜c⌝;⌜a⌝;⌜b⌝]⋅ THEN Auto)
         )
   THEN -1) }

1
1. EuclideanPlane
2. Point
3. Point
4. Point
5. Point
6. Point
7. Point
8. ab
9. xy
10. ab ≅ xy
11. Point
12. Colinear(a;b;p) ∧ ab  ⊥pc
⊢ ∃z:Point. (Cong3(abc,xyz) ∧ xy ∧ (u leftof xy ⇐⇒ leftof xy))


Latex:


Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c,x,y,u:Point.
    (c  \#  ab
    {}\mRightarrow{}  u  \#  xy
    {}\mRightarrow{}  ab  \mcong{}  xy
    {}\mRightarrow{}  (\mexists{}z:Point.  (Cong3(abc,xyz)  \mwedge{}  z  \#  xy  \mwedge{}  (u  leftof  xy  \mLeftarrow{}{}\mRightarrow{}  z  leftof  xy))))


By


Latex:
(Auto
  THEN  (InstLemma  `Euclid-drop-perp-1`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}
              THENA  (Auto  THEN  InstLemma    `lsep-iff-all-sep`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}  THEN  Auto)
              )
  THEN  D  -1)




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