Nuprl Lemma : stable__colinear
∀e:GeometryPrimitives. ∀[a,b,c:Point]. Stable{Colinear(a;b;c)}
Proof
Definitions occuring in Statement :
geo-colinear: Colinear(a;b;c),
geo-primitives: GeometryPrimitives,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-colinear: Colinear(a;b;c),
prop: ℙ,
and: P ∧ Q,
stable: Stable{P},
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
stable__not,
not_wf,
geo-between_wf,
geo-colinear_wf,
geo-point_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
isect_memberEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
voidElimination
Latex:
\mforall{}e:GeometryPrimitives. \mforall{}[a,b,c:Point]. Stable\{Colinear(a;b;c)\}
Date html generated:
2017_10_02-PM-03_26_03
Last ObjectModification:
2017_08_12-PM-07_42_00
Theory : euclidean!plane!geometry
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