Nuprl Lemma : eu-length-null-segment
∀[e:EuclideanPlane]. ∀[a:Point]. (|aa| = X ∈ {p:Point| O_X_p} )
Proof
Definitions occuring in Statement :
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,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-length: |s|,
all: ∀x:A. B[x],
top: Top,
euclidean-plane: EuclideanPlane,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a
Lemmas referenced :
eu_seg1_mk_seg_lemma,
eu_seg2_mk_seg_lemma,
eu-extend-property,
eu-O_wf,
eu-not-colinear-OXY,
eu-X_wf,
not_wf,
equal_wf,
eu-point_wf,
eu-extend_wf,
and_wf,
eu-between-eq_wf,
eu-congruent_wf,
euclidean-plane_wf,
eu-between-eq-trivial-right,
eu-congruent-iff-length,
eu-congruence-identity,
eu-mk-seg_wf,
eu-segment_wf,
eu-length_wf,
eu-construction-unicity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
isectElimination,
setElimination,
rename,
productElimination,
dependent_set_memberEquality,
because_Cache,
lambdaFormation,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality,
independent_isectElimination,
independent_pairFormation,
applyEquality,
lambdaEquality,
setEquality
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a:Point]. (|aa| = X)
Date html generated:
2016_05_18-AM-06_38_04
Last ObjectModification:
2015_12_28-AM-09_24_43
Theory : euclidean!geometry
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