Nuprl Lemma : stable__eu-between
∀e:EuclideanStructure. ∀[a,b,c:Point]. Stable{a-b-c}
Proof
Definitions occuring in Statement :
eu-between: a-b-c,
eu-point: Point,
euclidean-structure: EuclideanStructure,
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],
euclidean-structure: EuclideanStructure,
record+: record+,
member: t ∈ T,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
guard: {T},
prop: ℙ,
spreadn: spread3,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
eu-between: a-b-c,
stable: Stable{P},
not: ¬A,
false: False,
eu-point: Point
Lemmas referenced :
subtype_rel_self,
not_wf,
equal_wf,
uall_wf,
iff_wf,
and_wf,
isect_wf,
eu-point_wf,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
dependentIntersectionElimination,
sqequalRule,
dependentIntersectionEqElimination,
thin,
cut,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
lemma_by_obid,
isectElimination,
universeEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
cumulativity,
hypothesisEquality,
because_Cache,
setEquality,
productEquality,
productElimination,
setElimination,
rename,
introduction,
dependent_functionElimination,
voidElimination,
independent_isectElimination
Latex:
\mforall{}e:EuclideanStructure. \mforall{}[a,b,c:Point]. Stable\{a-b-c\}
Date html generated:
2016_05_18-AM-06_32_24
Last ObjectModification:
2015_12_28-AM-09_28_43
Theory : euclidean!geometry
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