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)))


Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-between-eq: a_b_c eu-congruent: ab=cd eu-point: Point uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] not: ¬A equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a prop: 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

\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

Home Index