Nuprl Lemma : stable__colinear
∀e:EuclideanStructure. ∀[a,b,c:Point]. Stable{Colinear(a;b;c)}
Proof
Definitions occuring in Statement :
eu-colinear: Colinear(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],
stable: Stable{P},
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
not_wf,
eu-colinear_wf,
eu-colinear-def,
and_wf,
equal_wf,
eu-point_wf,
eu-between_wf,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesis,
rename,
independent_functionElimination,
impliesFunctionality,
productElimination,
promote_hyp,
independent_pairFormation
Latex:
\mforall{}e:EuclideanStructure. \mforall{}[a,b,c:Point]. Stable\{Colinear(a;b;c)\}
Date html generated:
2016_05_18-AM-06_32_45
Last ObjectModification:
2015_12_28-AM-09_28_25
Theory : euclidean!geometry
Home
Index