Nuprl Lemma : stable__geo-midpoint
∀e:BasicGeometry. ∀[m,a,b:Point]. Stable{a=m=b}
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
basic-geometry: BasicGeometry,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
basic-geometry: BasicGeometry,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
geo-midpoint: a=m=b
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
stable__geo-congruent,
stable__geo-between,
geo-congruent_wf,
geo-between_wf,
stable__and
Rules used in proof :
independent_isectElimination,
instantiate,
rename,
setElimination,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[m,a,b:Point]. Stable\{a=m=b\}
Date html generated:
2017_10_02-PM-04_45_40
Last ObjectModification:
2017_08_05-AM-11_45_48
Theory : euclidean!plane!geometry
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