### Nuprl Lemma : eu-colinear-implies-1

`∀e:EuclideanPlane. ∀x,a,b:Point.  (Colinear(b;a;x) `` Colinear(b;a;a))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-colinear: `Colinear(a;b;c)` eu-point: `Point` all: `∀x:A. B[x]` implies: `P `` Q`
Definitions unfolded in proof :  rev_implies: `P `` Q` false: `False` not: `¬A` iff: `P `⇐⇒` Q` cand: `A c∧ B` and: `P ∧ Q` euclidean-plane: `EuclideanPlane` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` implies: `P `` Q` all: `∀x:A. B[x]`
Lemmas referenced :  eu-colinear_wf eu-point_wf euclidean-plane_wf eu-colinear-def not_wf equal_wf member_wf eu-between_wf
Rules used in proof :  productEquality voidElimination independent_pairFormation independent_functionElimination productElimination dependent_functionElimination because_Cache hypothesis hypothesisEquality rename setElimination thin isectElimination sqequalHypSubstitution lemma_by_obid cut lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}x,a,b:Point.    (Colinear(b;a;x)  {}\mRightarrow{}  Colinear(b;a;a))

Date html generated: 2016_05_18-AM-06_35_47
Last ObjectModification: 2016_01_04-AM-11_09_33

Theory : euclidean!geometry

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