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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