### Nuprl Lemma : eu-colinear-switch2

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

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 :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` euclidean-plane: `EuclideanPlane` uall: `∀[x:A]. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` false: `False` prop: `ℙ` eu-colinear-set: `eu-colinear-set(e;L)` l_all: `(∀x∈L.P[x])` top: `Top` int_seg: `{i..j-}` lelt: `i ≤ j < k` le: `A ≤ B` less_than': `less_than'(a;b)` less_than: `a < b` squash: `↓T` true: `True` select: `L[n]` cons: `[a / b]` subtract: `n - m`
Lemmas referenced :  euclidean-plane_wf eu-colinear_wf lelt_wf false_wf length_of_nil_lemma length_of_cons_lemma eu-colinear-is-colinear-set eu-point_wf equal_wf eu-colinear-def
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename hypothesisEquality isectElimination hypothesis productElimination independent_functionElimination equalitySymmetry voidElimination because_Cache sqequalRule isect_memberEquality voidEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation introduction imageMemberEquality baseClosed

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

Date html generated: 2016_05_18-AM-06_44_19
Last ObjectModification: 2016_01_16-PM-10_28_34

Theory : euclidean!geometry

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