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

`∀e:EuclideanPlane. ∀[p:{p:Point| O_X_p} ]. ∀[a:Point].  uiff(p < |aa|;False)`

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` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` false: `False` set: `{x:A| B[x]} `
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` eu-lt: `p < q` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` member: `t ∈ T` false: `False` not: `¬A` implies: `P `` Q` label: `...\$L... t` guard: `{T}` subtype_rel: `A ⊆r B` euclidean-plane: `EuclideanPlane` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  eu-point_wf eu-between-eq_wf eu-O_wf eu-X_wf equal_functionality_wrt_subtype_rel2 eu-length_wf eu-mk-seg_wf not_wf equal_wf false_wf eu-le-null-segment and_wf eu-le_wf uiff_wf set_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut independent_pairFormation introduction sqequalHypSubstitution productElimination thin hypothesis independent_functionElimination lambdaEquality setElimination rename hypothesisEquality setEquality lemma_by_obid isectElimination dependent_functionElimination because_Cache equalityTransitivity equalitySymmetry independent_isectElimination voidElimination sqequalRule productEquality equalityEquality applyEquality independent_pairEquality axiomEquality addLevel cumulativity

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[p:\{p:Point|  O\_X\_p\}  ].  \mforall{}[a:Point].    uiff(p  <  |aa|;False)

Date html generated: 2016_05_18-AM-06_38_10
Last ObjectModification: 2015_12_28-AM-09_25_57

Theory : euclidean!geometry

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