Nuprl Lemma : sq_stable__midpoint
∀e:EuclideanPlaneStructure. ∀[a,b,c:Point]. SqStable(a=c=b)
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
geo-midpoint: a=m=b,
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],
geo-midpoint: a=m=b,
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
sq_stable__and,
geo-between_wf,
geo-congruent_wf,
euclidean-plane-structure-subtype,
sq_stable__geo-between,
sq_stable__geo-congruent,
geo-point_wf,
euclidean-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
isect_memberEquality_alt,
universeIsType,
independent_functionElimination,
dependent_functionElimination,
inhabitedIsType
Latex:
\mforall{}e:EuclideanPlaneStructure. \mforall{}[a,b,c:Point]. SqStable(a=c=b)
Date html generated:
2019_10_16-PM-01_13_45
Last ObjectModification:
2018_10_28-AM-11_32_41
Theory : euclidean!plane!geometry
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