Nuprl Lemma : eu-congruent-between-implies-equal

e:EuclideanPlane. ∀[a,b,c,x:Point].  (b x ∈ Point) supposing (a_b_c and ab=ax and bc=xc)


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] equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a stable: Stable{P} not: ¬A implies:  Q prop: euclidean-plane: EuclideanPlane false: False uiff: uiff(P;Q) and: P ∧ Q
Lemmas referenced :  stable_point-eq eu-between-eq_wf eu-congruent_wf eu-congruence-identity-sym equal_wf eu-point_wf not_wf euclidean-plane_wf eu-congruent-refl eu-congruent-iff-length eu-length-flip eu-inner-five-segment
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis independent_isectElimination independent_functionElimination promote_hyp equalitySymmetry hyp_replacement Error :applyLambdaEquality,  setElimination rename because_Cache sqequalRule voidElimination isect_memberEquality axiomEquality equalityTransitivity dependent_functionElimination productElimination

\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,x:Point].    (b  =  x)  supposing  (a\_b\_c  and  ab=ax  and  bc=xc)

Date html generated: 2016_10_26-AM-07_42_26
Last ObjectModification: 2016_07_12-AM-08_08_42

Theory : euclidean!geometry

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