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Step * 1 of Lemma eu-be-end-eq


1. e : EuclideanPlane@i'
2. a : Point@i
3. b : Point@i
4. c : Point@i
5. a_b_c@i
6. ab=ac@i
⊢ b = c ∈ Point
BY
{ (InstLemma `eu-add-length-between` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THENA Auto)
THEN (InstLemma `eu-congruent-iff-length` [⌜e⌝;⌜a⌝;⌜b⌝;⌜a⌝;⌜c⌝]⋅ THENA Auto) }

1
1. e : EuclideanPlane@i'
2. a : Point@i
3. b : Point@i
4. c : Point@i
5. a_b_c@i
6. ab=ac@i
7. |ac| = |ab| + |bc| ∈ {p:Point| O_X_p} 
8. uiff(ab=ac;|ab| = |ac| ∈ {p:Point| O_X_p} )
⊢ b = c ∈ 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.  a\_b\_c@i
6.  ab=ac@i
\mvdash{}  b  =  c


By

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Latex:
(InstLemma  `eu-add-length-between`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THENA  Auto)
THEN  (InstLemma  `eu-congruent-iff-length`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THENA  Auto)

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