Nuprl Lemma : geo-zero-length_wf
∀[e:BasicGeometry]. (0 ∈ Length)
Proof
Definitions occuring in Statement :
geo-zero-length: 0,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
geo-length-type: Length,
prop: ℙ,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
geo-zero-length: 0
Lemmas referenced :
basic-geometry_wf,
quotient-member-eq,
geo-eq_weakening,
geo-between-trivial,
geo-length-equiv,
geo-eq_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf
Rules used in proof :
extract_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_set_memberEquality,
lambdaFormation,
lambdaEquality,
rename,
setElimination,
dependent_functionElimination,
because_Cache,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
setEquality
Latex:
\mforall{}[e:BasicGeometry]. (0 \mmember{} Length)
Date html generated:
2017_10_02-PM-04_45_31
Last ObjectModification:
2017_08_05-AM-09_09_51
Theory : euclidean!plane!geometry
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