Nuprl Lemma : stable__geo-ge
∀[g:GeometryPrimitives]. ∀[c,d,a,b:Point]. Stable{cd ≥ ab}
Proof
Definitions occuring in Statement :
geo-ge: ab ≥ cd,
geo-primitives: GeometryPrimitives,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
false: False,
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
stable: Stable{P},
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-ge: ab ≥ cd
Lemmas referenced :
geo-primitives_wf,
geo-point_wf,
geo-gt-prim_wf,
stable__not
Rules used in proof :
voidElimination,
universeIsType,
isectIsTypeImplies,
inhabitedIsType,
functionIsTypeImplies,
because_Cache,
dependent_functionElimination,
lambdaEquality_alt,
isect_memberEquality_alt,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[g:GeometryPrimitives]. \mforall{}[c,d,a,b:Point]. Stable\{cd \mgeq{} ab\}
Date html generated:
2019_10_29-AM-09_12_35
Last ObjectModification:
2019_10_25-PM-01_31_28
Theory : euclidean!plane!geometry
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