Nuprl Lemma : sq_stable__colinear
∀e:GeometryPrimitives. ∀[a,b,c:Point]. SqStable(Colinear(a;b;c))
Proof
Definitions occuring in Statement :
geo-colinear: Colinear(a;b;c),
geo-primitives: GeometryPrimitives,
geo-point: Point,
sq_stable: SqStable(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,
implies: P ⇒ Q,
sq_stable: SqStable(P),
geo-colinear: Colinear(a;b;c),
not: ¬A,
false: False,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
sq_stable__from_stable,
geo-colinear_wf,
stable__colinear,
not_wf,
geo-between_wf,
squash_wf,
geo-point_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
because_Cache,
productEquality,
isect_memberEquality,
voidElimination
Latex:
\mforall{}e:GeometryPrimitives. \mforall{}[a,b,c:Point]. SqStable(Colinear(a;b;c))
Date html generated:
2017_10_02-PM-03_26_04
Last ObjectModification:
2017_08_12-PM-07_42_08
Theory : euclidean!plane!geometry
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