### Nuprl Lemma : euclid-P2

`∀e:EuclideanPlane. ∀A,B,C:Point.  ∃L:Point. AL=BC supposing ¬(A = B ∈ Point)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-congruent: `ab=cd` eu-point: `Point` uimplies: `b supposing a` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` not: `¬A` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uimplies: `b supposing a` member: `t ∈ T` not: `¬A` implies: `P `` Q` false: `False` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` prop: `ℙ` and: `P ∧ Q` exists: `∃x:A. B[x]`
Lemmas referenced :  eu-point_wf not_wf equal_wf euclidean-plane_wf eu-congruent_wf eu-extend-exists
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_functionElimination equalitySymmetry dependent_set_memberEquality productElimination dependent_pairFormation

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}A,B,C:Point.    \mexists{}L:Point.  AL=BC  supposing  \mneg{}(A  =  B)

Date html generated: 2016_05_18-AM-06_45_58
Last ObjectModification: 2015_12_28-AM-09_21_53

Theory : euclidean!geometry

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