Nuprl Lemma : eu-congruent-preserves-between

e:EuclideanPlane. ∀[a,b,c,a',b',c':Point].  (a'_b'_c') supposing (bc=b'c' and ac=a'c' and ab=a'b' and a_b_c)


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]
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T euclidean-plane: EuclideanPlane stable: Stable{P} not: ¬A implies:  Q prop: false: False exists: x:A. B[x] and: P ∧ Q uiff: uiff(P;Q)
Lemmas referenced :  stable__eu-between-eq not_wf eu-between-eq_wf eu-congruent_wf eu-point_wf euclidean-plane_wf equal_wf eu-congruence-identity-sym eu-between-eq-trivial-left eu-congruent-between-exists 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 cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename hypothesisEquality hypothesis isectElimination independent_isectElimination because_Cache independent_functionElimination voidElimination promote_hyp equalitySymmetry hyp_replacement Error :applyLambdaEquality,  sqequalRule productElimination equalityTransitivity

    \mforall{}[a,b,c,a',b',c':Point].    (a'\_b'\_c')  supposing  (bc=b'c'  and  ac=a'c'  and  ab=a'b'  and  a\_b\_c)

Date html generated: 2016_10_26-AM-07_42_36
Last ObjectModification: 2016_07_12-AM-08_08_56

Theory : euclidean!geometry

Home Index