### Nuprl Lemma : eu-construction-unicity

`∀e:EuclideanPlane. ∀[Q,A,X,Y:Point].  (X = Y ∈ Point) supposing (AY=AX and Q_A_X and Q_A_Y and (¬(Q = A ∈ Point)))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-congruent: `ab=cd` eu-point: `Point` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` not: `¬A` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` prop: `ℙ` euclidean-plane: `EuclideanPlane`
Lemmas referenced :  eu-congruent_wf eu-between-eq_wf not_wf equal_wf eu-point_wf euclidean-plane_wf eu-congruent-refl eu-five-segment eu-congruence-identity eu-congruent-symmetry eu-three-segment
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation introduction cut hypothesis lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination independent_isectElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[Q,A,X,Y:Point].    (X  =  Y)  supposing  (AY=AX  and  Q\_A\_X  and  Q\_A\_Y  and  (\mneg{}(Q  =  A)))

Date html generated: 2016_05_18-AM-06_35_23
Last ObjectModification: 2015_12_28-AM-09_26_46

Theory : euclidean!geometry

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