Nuprl Lemma : Euclid-Prop10-ext
∀e:EuclideanPlane. ∀a:Point. ∀b:{b:Point| a ≠ b} . (∃d:Point [(a-d-b ∧ ad ≅ db)])
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-strict-between: a-b-c,
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 :
Euclid-midpoint,
Euclid-Prop10,
member: t ∈ T
Lemmas referenced :
Euclid-Prop10,
Euclid-midpoint
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}b:\{b:Point| a \mneq{} b\} . (\mexists{}d:Point [(a-d-b \mwedge{} ad \mcong{} db)])
Date html generated:
2018_05_22-PM-00_08_10
Last ObjectModification:
2018_05_21-AM-01_16_47
Theory : euclidean!plane!geometry
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