Nuprl Lemma : eu-between-trans
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. (a-b-c) supposing (b-c-d and a-b-d)
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,
euclidean-plane: EuclideanPlane,
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
guard: {T}
Lemmas referenced :
euclidean-plane_wf,
eu-point_wf,
eu-between_wf,
sq_stable__eu-between
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
introduction,
productElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. (a-b-c) supposing (b-c-d and a-b-d)
Date html generated:
2016_05_18-AM-06_33_47
Last ObjectModification:
2016_01_16-PM-10_31_46
Theory : euclidean!geometry
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