Nuprl Lemma : geo-length-sep_wf
∀[g:GeometryPrimitives]. ∀[a,b,c,d:Point]. (ab # cd) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-length-sep: ab # cd),
geo-primitives: GeometryPrimitives,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
or: P ∨ Q,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
geo-point: Point,
geo-gt-prim: ab>cd),
geo-length-sep: ab # cd),
geo-primitives: GeometryPrimitives,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-primitives_wf,
istype-atom,
top_wf,
record-select_wf,
subtype_rel_self
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
axiomEquality,
hypothesisEquality,
unionEquality,
equalitySymmetry,
equalityTransitivity,
lambdaEquality_alt,
cumulativity,
functionEquality,
universeEquality,
isectElimination,
extract_by_obid,
instantiate,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
dependentIntersectionElimination,
sqequalRule,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:GeometryPrimitives]. \mforall{}[a,b,c,d:Point]. (ab \# cd) \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-09_12_17
Last ObjectModification:
2019_10_25-PM-01_26_20
Theory : euclidean!plane!geometry
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