Nuprl Lemma : eu-be-neq
∀e:EuclideanPlane. ∀a,b,c:Point. ((¬(a = b ∈ Point)) ⇒ a_b_c ⇒ (¬(a = c ∈ Point)))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
uimplies: b supposing a
Lemmas referenced :
eu-between-eq_wf,
eu-between-eq-same,
equal_wf,
eu-point_wf,
not_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
equalitySymmetry,
hypothesis,
hyp_replacement,
Error :applyLambdaEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesisEquality,
sqequalRule,
independent_isectElimination,
independent_functionElimination,
voidElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. ((\mneg{}(a = b)) {}\mRightarrow{} a\_b\_c {}\mRightarrow{} (\mneg{}(a = c)))
Date html generated:
2016_10_26-AM-07_44_43
Last ObjectModification:
2016_07_12-AM-08_11_16
Theory : euclidean!geometry
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