Nuprl Lemma : geo-extend-construction-ext
∀e:EuclideanPlane. ∀q:Point. ∀a:{a:Point| q ≠ a} . ∀b,c:Point. (∃x:{Point| (q_a_x ∧ ax ≅ bc)})
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-between: a_b_c,
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,
geo-extend-construction,
extend-using-SC,
Euclid-Prop2-ext,
ifthenelse: if b then t else f fi
Lemmas referenced :
geo-extend-construction,
extend-using-SC,
Euclid-Prop2-ext
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{}q:Point. \mforall{}a:\{a:Point| q \mneq{} a\} . \mforall{}b,c:Point. (\mexists{}x:\{Point| (q\_a\_x \mwedge{} ax \00D0 bc)\})
Date html generated:
2017_10_02-PM-04_50_10
Last ObjectModification:
2017_08_09-PM-06_40_07
Theory : euclidean!plane!geometry
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