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


1. e : BasicGeometry
2. a : Point
3. b : Point
4. c : Point
5. a_b_c
6. ab ≅ ac
⊢ b ≡ c
BY
{ (InstLemma `geo-add-length-between` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THENA Auto)
THEN (InstLemma `geo-congruent-iff-length` [⌜e⌝;⌜a⌝;⌜b⌝;⌜a⌝;⌜c⌝]⋅ THENA Auto) }

1
1. e : BasicGeometry
2. a : Point
3. b : Point
4. c : Point
5. a_b_c
6. ab ≅ ac
7. |ac| = |ab| + |bc| ∈ Length
8. uiff(ab ≅ ac;|ab| = |ac| ∈ Length)
⊢ b ≡ c

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  a\_b\_c
6.  ab  \mcong{}  ac
\mvdash{}  b  \mequiv{}  c


By

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