### Nuprl Lemma : eu-between-eq-exchange4

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

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]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` Q` stable: `Stable{P}` not: `¬A` and: `P ∧ Q` prop: `ℙ` false: `False` squash: `↓T`
Lemmas referenced :  sq_stable__eu-between-eq stable__eu-between-eq eu-between-eq-symmetry eu-between-eq-inner-trans eu-between-eq-exchange3 and_wf equal_wf eu-point_wf eu-between-eq_wf not_wf euclidean-plane_wf eu-between-eq-outer-trans
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 equalitySymmetry dependent_set_memberEquality independent_pairFormation applyEquality lambdaEquality productElimination setEquality hyp_replacement Error :applyLambdaEquality,  sqequalRule voidElimination imageMemberEquality baseClosed imageElimination comment

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

Date html generated: 2016_10_26-AM-07_41_17
Last ObjectModification: 2016_07_12-AM-08_07_30

Theory : euclidean!geometry

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