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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