Nuprl Lemma : eu-not-equal-OXY
∀[e:EuclideanStructure]. ((¬(O = X ∈ Point)) ∧ (¬(O = Y ∈ Point)) ∧ (¬(X = Y ∈ Point)))
Proof
Definitions occuring in Statement :
eu-Y: Y,
eu-X: X,
eu-O: O,
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,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
all: ∀x:A. B[x],
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
eu-not-colinear-OXY,
equal_wf,
eu-point_wf,
eu-O_wf,
eu-X_wf,
eu-colinear_wf,
eu-Y_wf,
euclidean-structure_wf,
not_wf,
member_wf,
eu-between_wf,
eu-colinear-def
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
productElimination,
independent_functionElimination,
voidElimination,
dependent_functionElimination,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
sqequalRule,
because_Cache,
equalityTransitivity,
productEquality
Latex:
\mforall{}[e:EuclideanStructure]. ((\mneg{}(O = X)) \mwedge{} (\mneg{}(O = Y)) \mwedge{} (\mneg{}(X = Y)))
Date html generated:
2016_10_26-AM-07_40_40
Last ObjectModification:
2016_07_12-AM-08_06_42
Theory : euclidean!geometry
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