### 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|)`

Proof

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: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` false: `False` set: `{x:A| B[x]} ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` false: `False` prop: `ℙ` 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

Latex:
\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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