Nuprl Lemma : eu-colinear-five-segment

`∀e:EuclideanPlane`
`  ∀[a,b,c,d,A,B,C,D:Point].  (cd=CD) supposing (bd=BD and ad=AD and bc=BC and ab=AB and ac=AC and Colinear(a;b;c))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-colinear: `Colinear(a;b;c)` eu-congruent: `ab=cd` 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` member: `t ∈ T` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` Q` and: `P ∧ Q` prop: `ℙ` not: `¬A` false: `False` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)`
Lemmas referenced :  sq_stable__eu-congruent eu-colinear-cases eu-congruent_wf stable__eu-congruent not_wf equal_wf eu-point_wf eu-between_wf eu-colinear_wf euclidean-plane_wf eu-congruence-identity-sym eu-between-eq-def eu-congruent-preserves-between eu-congruent-iff-length eu-length-flip eu-five-segment eu-between-eq-symmetry eu-inner-five-segment
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename because_Cache hypothesis isectElimination hypothesisEquality independent_functionElimination productElimination productEquality equalityEquality voidElimination sqequalRule imageMemberEquality baseClosed imageElimination equalitySymmetry hyp_replacement Error :applyLambdaEquality,  independent_isectElimination promote_hyp equalityTransitivity

Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,d,A,B,C,D:Point].
(cd=CD)  supposing  (bd=BD  and  ad=AD  and  bc=BC  and  ab=AB  and  ac=AC  and  Colinear(a;b;c))

Date html generated: 2016_10_26-AM-07_42_42
Last ObjectModification: 2016_07_12-AM-08_09_03

Theory : euclidean!geometry

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