Nuprl Lemma : eu-between-eq-inner-trans

e:EuclideanPlane. ∀[a,b,c,d:Point].  (a_b_c) supposing (b_c_d and a_b_d)


Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-between-eq: a_b_c eu-point: Point uimplies: 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: supposing a member: t ∈ T euclidean-plane: EuclideanPlane sq_stable: SqStable(P) implies:  Q stable: Stable{P} not: ¬A false: False prop: squash: T iff: ⇐⇒ Q and: P ∧ Q rev_implies:  Q cand: c∧ B true: True subtype_rel: A ⊆B guard: {T}
Lemmas referenced :  sq_stable__eu-between-eq stable__eu-between-eq not_wf eu-between-eq_wf eu-point_wf euclidean-plane_wf eu-between-eq-def equal_wf eu-between_wf eu-between-trans stable__eu-between squash_wf true_wf euclidean-structure_wf iff_weakening_equal eu-between-same and_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename because_Cache hypothesis isectElimination hypothesisEquality independent_functionElimination independent_isectElimination addLevel voidElimination levelHypothesis sqequalRule imageMemberEquality baseClosed imageElimination productElimination productEquality independent_pairFormation equalitySymmetry equalityTransitivity applyEquality lambdaEquality universeEquality natural_numberEquality hyp_replacement dependent_set_memberEquality setEquality

\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,d:Point].    (a\_b\_c)  supposing  (b\_c\_d  and  a\_b\_d)

Date html generated: 2016_10_26-AM-07_40_59
Last ObjectModification: 2016_07_12-AM-08_07_10

Theory : euclidean!geometry

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