Nuprl Lemma : eu-colinear-equidistant
∀e:EuclideanPlane. ∀[a,b,c,p,q:Point]. (cp=cq) supposing (ap=aq and bp=bq and Colinear(a;b;c))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-colinear: Colinear(a;b;c),
eu-congruent: ab=cd,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
eu-colinear-five-segment,
sq_stable__eu-congruent,
eu-congruent-refl,
euclidean-plane_wf,
eu-point_wf,
eu-colinear_wf,
eu-congruent_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
introduction,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,p,q:Point]. (cp=cq) supposing (ap=aq and bp=bq and Colinear(a;b;c))
Date html generated:
2016_05_18-AM-06_39_15
Last ObjectModification:
2016_01_16-PM-10_29_09
Theory : euclidean!geometry
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