Nuprl Lemma : eu-between-eq-implies-colinear3

e:EuclideanPlane. ∀[a,b,c:Point].  (Colinear(a;b;c)) supposing (b_c_a and (a b ∈ Point)))


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

\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c:Point].    (Colinear(a;b;c))  supposing  (b\_c\_a  and  (\mneg{}(a  =  b)))

Date html generated: 2016_05_18-AM-06_33_57
Last ObjectModification: 2015_12_28-AM-09_28_36

Theory : euclidean!geometry

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