Nuprl Lemma : eu-not-colinear-OXY
∀[e:EuclideanStructure]. ((¬(O = X ∈ Point)) ∧ (¬Colinear(O;X;Y)))
Proof
Definitions occuring in Statement :
eu-Y: Y,
eu-X: X,
eu-O: O,
eu-colinear: Colinear(a;b;c),
eu-point: Point,
euclidean-structure: EuclideanStructure,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-Y: Y,
eu-X: X,
eu-O: O,
spreadn: spread3,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
eu-nontrivial_wf,
eu-point_wf,
not_wf,
equal_wf,
eu-colinear_wf,
eu-O_wf,
eu-X_wf,
eu-Y_wf,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setEquality,
productEquality,
because_Cache,
productElimination,
sqequalRule,
lambdaFormation,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_pairEquality,
lambdaEquality,
voidElimination,
independent_pairFormation,
setElimination,
rename
Latex:
\mforall{}[e:EuclideanStructure]. ((\mneg{}(O = X)) \mwedge{} (\mneg{}Colinear(O;X;Y)))
Date html generated:
2016_05_18-AM-06_32_52
Last ObjectModification:
2015_12_28-AM-09_28_06
Theory : euclidean!geometry
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