Nuprl Lemma : Euclid-Prop1-left-ext
∀e:EuclideanPlane. ∀a:Point. ∀b:{b:Point| a ≠ b} . (∃c:Point [(((cb ≅ ab ∧ ca ≅ ba) ∧ ca ≅ cb) ∧ c leftof ab)])
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-congruent: ab ≅ cd,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
member: t ∈ T,
eqtri: Δ(a;b),
Euclid-Prop1-left,
geo-CC-2,
sq_stable__geo-sep,
geo-congruent-refl
Lemmas referenced :
Euclid-Prop1-left,
geo-CC-2,
sq_stable__geo-sep,
geo-congruent-refl
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}b:\{b:Point| a \mneq{} b\} .
(\mexists{}c:Point [(((cb \mcong{} ab \mwedge{} ca \mcong{} ba) \mwedge{} ca \mcong{} cb) \mwedge{} c leftof ab)])
Date html generated:
2018_05_22-AM-11_53_45
Last ObjectModification:
2018_03_30-AM-10_01_33
Theory : euclidean!plane!geometry
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