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Step * 2 2 of Lemma eu-sum-eq-x


1. e : EuclideanPlane@i'
2. a : Point@i
3. b : Point@i
4. c : Point@i
5. d : Point@i
6. X = |ab| + |cd| ∈ {p:Point| O_X_p} @i
7. |cd| ≤ X
⊢ c = d ∈ Point
BY
{ InstLemma `eu-le-null-segment` [⌜e⌝;⌜|cd|⌝;⌜a⌝]⋅
THEN Assert ⌜|aa| = X ∈ {p:Point| O_X_p} ⌝⋅
THEN InstLemma `eu-length-null-segment` [⌜e⌝;⌜a⌝]⋅
THEN Auto }

1
1. e : EuclideanPlane@i'
2. a : Point@i
3. b : Point@i
4. c : Point@i
5. d : Point@i
6. X = |ab| + |cd| ∈ {p:Point| O_X_p} @i
7. |cd| ≤ X
8. |cd| = |aa| ∈ {p:Point| O_X_p}  supposing |cd| ≤ |aa|
9. |cd| ≤ |aa| supposing |cd| = |aa| ∈ {p:Point| O_X_p} 
10. |aa| = X ∈ {p:Point| O_X_p} 
11. |aa| = X ∈ {p:Point| O_X_p} 
⊢ c = d ∈ Point

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Latex:

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Latex:

1.  e  :  EuclideanPlane@i'
2.  a  :  Point@i
3.  b  :  Point@i
4.  c  :  Point@i
5.  d  :  Point@i
6.  X  =  |ab|  +  |cd|@i
7.  |cd|  \mleq{}  X
\mvdash{}  c  =  d


By

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Latex:
InstLemma  `eu-le-null-segment`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}|cd|\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}
THEN  Assert  \mkleeneopen{}|aa|  =  X\mkleeneclose{}\mcdot{}
THEN  InstLemma  `eu-length-null-segment`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}
THEN  Auto

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