Nuprl Lemma : trivial-zero-length
∀[e:BasicGeometry]. ∀[a:Point]. (|aa| = 0 ∈ Length)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-zero-length: 0,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
basic-geometry: BasicGeometry,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
geo-zero-length-iff,
geo-eq_weakening,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
productElimination,
independent_functionElimination,
isectElimination,
independent_isectElimination,
hypothesis,
applyEquality,
instantiate,
sqequalRule,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a:Point]. (|aa| = 0)
Date html generated:
2018_05_22-AM-11_55_52
Last ObjectModification:
2018_04_10-PM-04_34_41
Theory : euclidean!plane!geometry
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