### Nuprl Lemma : eu-colinear-same-side2

`∀e:EuclideanPlane`
`  ∀[A,B,C,D:Point].  (Colinear(A;C;D)) supposing ((¬(A = C ∈ Point)) and (¬(A = B ∈ Point)) and A_B_C and A_B_D)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-colinear: `Colinear(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 :  prop: `ℙ` euclidean-plane: `EuclideanPlane` false: `False` implies: `P `` Q` not: `¬A` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` rev_implies: `P `` Q` and: `P ∧ Q` iff: `P `⇐⇒` Q` cand: `A c∧ B`
Lemmas referenced :  eu-between-eq-def eu-colinear-def eu-between_wf eu-between-eq-same-side eu-point_wf not_wf equal_wf eu-between-eq_wf euclidean-plane_wf
Rules used in proof :  rename setElimination equalityEquality voidElimination lambdaEquality sqequalRule introduction independent_isectElimination isectElimination isect_memberFormation hypothesisEquality thin dependent_functionElimination sqequalHypSubstitution hypothesis lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution lemma_by_obid cut because_Cache productEquality independent_pairFormation independent_functionElimination productElimination equalitySymmetry

Latex:
\mforall{}e:EuclideanPlane
\mforall{}[A,B,C,D:Point].    (Colinear(A;C;D))  supposing  ((\mneg{}(A  =  C))  and  (\mneg{}(A  =  B))  and  A\_B\_C  and  A\_B\_D)

Date html generated: 2016_05_18-AM-06_39_56
Last ObjectModification: 2016_01_01-PM-03_17_21

Theory : euclidean!geometry

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