Nuprl Lemma : eu-lt-null-segment2

e:EuclideanPlane. ∀[p:{p:Point| O_X_p} ]. ∀[a,b:Point].  (False) supposing ((a b ∈ Point) and p < |ab|)


Definitions occuring in Statement :  eu-lt: p < q 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 uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] false: False set: {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 false: False prop: euclidean-plane: EuclideanPlane so_lambda: λ2x.t[x] so_apply: x[s] uiff: uiff(P;Q) and: P ∧ Q
Lemmas referenced :  eu-lt_wf eu-between-eq_wf eu-O_wf eu-X_wf eu-length_wf eu-mk-seg_wf equal_wf eu-point_wf set_wf euclidean-plane_wf eu-lt-null-segment
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation introduction cut hypothesis equalitySymmetry thin hyp_replacement Error :applyLambdaEquality,  extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality setElimination rename dependent_set_memberEquality because_Cache dependent_functionElimination sqequalRule isect_memberEquality equalityTransitivity voidElimination lambdaEquality productElimination independent_isectElimination

\mforall{}e:EuclideanPlane.  \mforall{}[p:\{p:Point|  O\_X\_p\}  ].  \mforall{}[a,b:Point].    (False)  supposing  ((a  =  b)  and  p  <  |ab|)

Date html generated: 2016_10_26-AM-07_42_06
Last ObjectModification: 2016_07_12-AM-08_08_17

Theory : euclidean!geometry

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