### 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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