Nuprl Lemma : sq_stable__geo-strict-between
∀g:EuclideanPlaneStructure. ∀a,b,c:Point. SqStable(a-b-c)
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
geo-strict-between: a-b-c,
geo-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
geo-strict-between: a-b-c
Lemmas referenced :
euclidean-plane-structure_wf,
geo-point_wf,
sq_stable__geo-sep,
sq_stable__geo-between,
geo-sep_wf,
euclidean-plane-structure-subtype,
geo-between_wf,
sq_stable__and
Rules used in proof :
dependent_functionElimination,
independent_functionElimination,
because_Cache,
productEquality,
isect_memberEquality,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlaneStructure. \mforall{}a,b,c:Point. SqStable(a-b-c)
Date html generated:
2017_10_02-PM-03_26_42
Last ObjectModification:
2017_08_04-PM-06_45_41
Theory : euclidean!plane!geometry
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