### Nuprl Lemma : eu-length-null-segment

`∀[e:EuclideanPlane]. ∀[a:Point].  (|aa| = X ∈ {p:Point| O_X_p} )`

Proof

Definitions occuring in Statement :  eu-length: `|s|` eu-mk-seg: `ab` euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-X: `X` eu-O: `O` eu-point: `Point` uall: `∀[x:A]. B[x]` set: `{x:A| B[x]} ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` eu-length: `|s|` all: `∀x:A. B[x]` top: `Top` euclidean-plane: `EuclideanPlane` and: `P ∧ Q` prop: `ℙ` implies: `P `` Q` uiff: `uiff(P;Q)` uimplies: `b supposing a`
Lemmas referenced :  eu_seg1_mk_seg_lemma eu_seg2_mk_seg_lemma eu-extend-property eu-O_wf eu-not-colinear-OXY eu-X_wf not_wf equal_wf eu-point_wf eu-extend_wf and_wf eu-between-eq_wf eu-congruent_wf euclidean-plane_wf eu-between-eq-trivial-right eu-congruent-iff-length eu-congruence-identity eu-mk-seg_wf eu-segment_wf eu-length_wf eu-construction-unicity
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin isect_memberEquality voidElimination voidEquality hypothesis hypothesisEquality isectElimination setElimination rename productElimination dependent_set_memberEquality because_Cache lambdaFormation equalityEquality equalityTransitivity equalitySymmetry independent_functionElimination axiomEquality independent_isectElimination independent_pairFormation applyEquality lambdaEquality setEquality

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[a:Point].    (|aa|  =  X)

Date html generated: 2016_05_18-AM-06_38_04
Last ObjectModification: 2015_12_28-AM-09_24_43

Theory : euclidean!geometry

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