Nuprl Lemma : eu-between-trans2
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. (a-b-c) supposing (d-b-c and d-a-b)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between: a-b-c,
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
Lemmas referenced :
eu-between-trans,
eu-between-sym,
eu-between_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
independent_isectElimination,
hypothesis,
because_Cache,
setElimination,
rename
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. (a-b-c) supposing (d-b-c and d-a-b)
Date html generated:
2016_05_18-AM-06_33_52
Last ObjectModification:
2015_12_28-AM-09_27_46
Theory : euclidean!geometry
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