### Nuprl Lemma : eu-between-eq-outer-trans

`∀e:EuclideanPlane. ∀[a,b,c,d:Point].  (a_c_d) supposing (b_c_d and a_b_c and (¬(b = c ∈ Point)))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-point: `Point` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` not: `¬A` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` not: `¬A` implies: `P `` Q` false: `False` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` prop: `ℙ` exists: `∃x:A. B[x]` and: `P ∧ Q` squash: `↓T`
Lemmas referenced :  eu-point_wf sq_stable__eu-between-eq eu-between-eq_wf eu-between-eq-same equal_wf eu-extend-exists not_wf euclidean-plane_wf eu-construction-unicity eu-between-eq-symmetry eu-between-eq-inner-trans eu-between-eq-exchange3 eu-congruent-symmetry
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction sqequalRule sqequalHypSubstitution lambdaEquality dependent_functionElimination thin hypothesisEquality voidElimination equalityEquality extract_by_obid isectElimination setElimination rename hypothesis because_Cache independent_functionElimination equalitySymmetry hyp_replacement Error :applyLambdaEquality,  independent_isectElimination dependent_set_memberEquality productElimination imageMemberEquality baseClosed imageElimination

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

Date html generated: 2016_10_26-AM-07_41_13
Last ObjectModification: 2016_07_12-AM-08_07_23

Theory : euclidean!geometry

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